Based on the given information, Mike's grandmother deposited $6,000 into the savings account.
What is simple interest?
Simple interest is a method of calculating interest on a principal amount, where the interest is calculated only on the original amount of the loan or investment, without taking into account any interest that may have been previously earned. The formula for calculating simple interest is I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.
We are given that the interest rate is 8% and the interest earned after 10 years is $4,800. So we can write:
4,800 = P * 0.08 * 10
Simplifying the equation, we get:
4,800 = 0.8P
Dividing both sides by 0.8, we get:
P = 6,000
Therefore, Mike's grandmother deposited $6,000 into the savings account.
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type the problem below as an equivalent problem using common denominators then add and simplify your answer. 6 over 8 + 1 over 12
[tex]\frac{6}{8} + \frac{1}{12} = \frac{5}{6}[/tex] when added and simplified.
What is a fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).
To add fractions with different denominators, we need to first find a common denominator.
The common denominator of 8 and 12 is 24.
So we can rewrite the problem as:
6/8 + 1/12 =6×3/8×3 + 1×2/12×2 = 18/24 + 2/24 = 8/6 + 12/1
Now we can add the fractions:
18/24 + 2/24 = 20/24
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:
20/24 = 5/6
Therefore, [tex]\frac{6}{8} + \frac{1}{12} = \frac{5}{6}[/tex] when added and simplified.
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54÷3² + (2 x 6)-4
Show your solution...
Step-by-step explanation:
54÷9+12-4
=6+12-4
=14//
a connected planar graph has $26$ faces and $v$ vertices, and all its vertices have the same degree. what are all possible values of $v$?
All possible values of v are integers greater than or equal to 28.
In a connected planar graph with 26 faces, the number of edges can be found using Euler's formula, which states that v - e + f = 2 for any connected planar graph. Since the graph is connected and planar, we know that e = 3v/2 - 3 (using the handshaking lemma and Euler's formula), and substituting this into Euler's formula gives:
v - (3v/2 - 3) + 26 = 2
Simplifying this equation yields v = 52 - 2f.
Since all vertices have the same degree, each face must have degree at least 3, and the sum of the degrees of the faces is equal to 2 times the number of edges. Therefore, we have:
3f ≤ 2e = 3v - 6
f ≤ (3v - 6)/3 = v - 2
Combining this with the fact that there are 26 faces, we get:
26 ≤ v - 2
v ≥ 28
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A 9-pack of popsicles costs $4.77. What is the unit price?
Answer:$0.53
9 pack = $4.77
1 pack = $?
9÷1=9, $4.77÷9=$0.53
Answer: $0.53
Step-by-step explanation: 9 divided by 1 is 9 and 4.77 divided by 9 is 0.53. ;)
How do you graph (4,5) and (2,2) to find the distance between the pionts.
The distance between the points (4, 5) and (2, 2) is approximately 3.61 units.
What is the distance?
To find the distance between two points, we can use the distance formula:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Using the given points (4, 5) and (2, 2), we have:
distance = √[(2 - 4)² + (2 - 5)²]
= √[(-2)² + (-3)²]
= √[4 + 9]
= √13
So the distance between the points (4, 5) and (2, 2) is approximately 3.61 units.
To graph these points, we would plot them on a coordinate plane. The point (4, 5) would be two units to the right of the y-axis and five units up from the x-axis.
The point (2, 2) would be two units to the right of the y-axis and two units up from the x-axis. We could then use a ruler to measure the distance between the two points on the graph to verify that it is approximately 3.61 units.
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prove that ∆ABC=8 ∆EFG
Answer:
To prove that ∆ABC=8 ∆EFG, we need to use the concept of similarity of triangles and the ratio of their corresponding sides.
Given that ∆ABC and ∆EFG are similar triangles, we can write:
AB/EF = BC/FG = AC/EG = k (a constant)
Let's assume that AB = x, BC = y, and AC = z. Similarly, let EF = p, FG = q, and EG = r.
From the given information, we can write:
EF = AB/2 (since E is the midpoint of AB)
FG = BC/2 (since F is the midpoint of BC)
EG = AC/2 (since G is the midpoint of AC)
Substituting these values in the above equation, we get:
x/p = y/q = z/r = k
Now, let's consider the area of the triangles.
Area of ∆ABC = (1/2) * AB * BC * sin(∠BAC)
Area of ∆EFG = (1/2) * EF * FG * sin(∠EFG)
Using the values we have assumed earlier, we get:
Area of ∆ABC = (1/2) * x * y * sin(∠BAC)
Area of ∆EFG = (1/2) * (x/2) * (y/2) * sin(∠EFG)
Simplifying these expressions, we get:
Area of ∆ABC = (xy/2) * sin(∠BAC)
Area of ∆EFG = (xy/8) * sin(∠EFG)
Now, since the triangles are similar, their corresponding angles are equal. Therefore,
sin(∠BAC) / sin(∠EFG) = z/r
Substituting the value of k from earlier, we get:
sin(∠BAC) / sin(∠EFG) = 2k
Solving for sin(∠EFG), we get:
sin(∠EFG) = sin(∠BAC) / (2k)
Substituting this value in the expression for the area of ∆EFG, we get:
Area of ∆EFG = (xy/8) * (sin(∠BAC) / (2k))
Area of ∆EFG = (xy/16) * sin(∠BAC)
Now, substituting the value of the area of ∆ABC in this expression, we get:
Area of ∆EFG = (1/2) * Area of ∆ABC * (1/8)
Area of ∆EFG = (1/16) * Area of ∆ABC
Therefore, we have proved that ∆ABC=8 ∆EFG.
Step-by-step explanation:
Hey ! APPROVED ANSWER ITO.
Hey can y’all help me with this math question ??
Answer:
x ≤ 9
Step-by-step explanation:
See the picture below. The circle above the 9 is closed indicating that 9 is included. If 9 was not included you would have an open circle and the answer would have a < rather than a [tex]\leq[/tex] symbol
Helping in the name of Jesus.
a person 6 feet tall is walking away from a lamppost that is 15 ft tall at a rate of 6 ft/sec. at what rate is the end of the person's shadow moving away from the lamppost
The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.
Let us consider the the distance of the person from the bottom of the lamppost is = xft
therefore the length of shadow is = yft
then the formula is
x + y/15 = y/6
or, 6(x + y) = 15y
=> 6x + 6y = 15y
=> 9y = 6x
therefore, y = 2x/3
Differentiation of both sides w.r.t t
dy/dt = 2/3 × dx/dt
we know that,
dx/dt = 6 ft/sec
then,
dy/dt = 2/3 × 6 => 4 ft/sec
The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.
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Suppose that it rains in Spain an average of once every 13 days, and when it does, hurricanes have a 8% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 3% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? (Round your answer to four decimal places.)
the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.
what is bayes theorem ?
Let’s use Bayes’ theorem to solve this problem. Let A be the event that it rains in Spain and B be the event that hurricanes happen in Hartford. We want to find P(A|B). We know that P(B|A) = 0.08 and P(B|A’) = 0.03 where A’ is the complement of A (i.e., it does not rain in Spain). We also know that P(A) = 1/13 and P(A’) = 12/13.
Bayes’ theorem states that:
P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|A’) * P(A’)]
Substituting the values we have:
P(A|B) = (0.08 * 1/13) / [(0.08 * 1/13) + (0.03 * 12/13)] = 0.2192 (rounded to four decimal places)
Therefore, the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.
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A bell tolls every 30mins on the journey and at half past the hour. How many times does the bell toll between the times of 11.45am and 3.10pm
The bell tolls 6 times between 11:45 AM and 3:10 PM.
Determine how many times the bell tolls between 11:45 AM and 3:10 PM, follow these steps:
1. Calculate the time interval between 11:45 AM and 3:10 PM:
3:10 PM - 11:45 AM = 3 hours and 25 minutes
2. Find the next bell toll after 11:45 AM:
Since the bell tolls at half past the hour, the next bell toll is at 12:30 PM.
3. Calculate the time interval between 12:30 PM and 3:10 PM:
3:10 PM - 12:30 PM = 2 hours and 40 minutes
4. Divide the time interval by the bell's tolling interval:
2 hours and 40 minutes = 160 minutes
160 minutes / 30 minutes (bell's tolling interval) = 5.33
5. Since the bell can't toll a fraction of a time, round down the result:
5.33 rounds down to 5
6. Add 1 to the rounded result to include the bell toll at 12:30 PM:
5 + 1 = 6.
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5. Kenyi covers the front of a circular bulletin board with fabric that costs $1.48 per square foot. The bulletin board has radius 2.5 feet. Kenyi will count only the cost of the exact amount of fabric he uses. 7.G.4 Part A: Write the numbers to find the cost of the fabric that Kenyi needs to cover the front of the bulletin board. Use 3.14 for TT. Cost = Part B: What is the cost of the fabric? Round to the nearest cent. 1.25 2 3.14 1.48 2.5 5
Part A:
the cost of the fabric is 29.07
Part B:
Rounding to the nearest cent, the cost of the fabric is $29.07.
How do we calculate?we need to calculate the area of the front of the bulletin board and then multiply it by the cost per square foot in order to find the cost of the fabric.
The area of a circle with radius 2.5 feet is:
A = πr^2
A = 3.14 x 2.5^2
A = 19.625 square feet
So, the cost of the fabric is:
Cost = area x cost per square foot
Cost = 19.625 x 1.48
Cost = 29.07
Rounding to the nearest cent, the cost of the fabric is $29.07.
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Edwin deposited money into a savings account that pays a simple annual interest rate of 2.4%. He earned $23 in interest after 6 years. How much did he deposit? Round answer to the hundredths place
Edwin deposited $159.72 into the savings account.
What is interest?Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is usually expressed as an annual percentage rate, interest expense or revenue is frequently expressed as a dollar amount.(APR).
We can use the formula for simple interest to solve this problem:
simple interest = principal x rate x time
Where:
principal is the amount of money depositedrate is the annual interest rate (as a decimal)time is the duration of the investment (in years)We know the rate is 2.4% per year, which is equivalent to 0.024 as a decimal. We also know the time is 6 years, and the interest earned is $23. We can plug these values into the formula and solve for the principal:
23 = principal x 0.024 x 6
Simplifying:
23 = 0.144 x principal
Dividing both sides by 0.144:
principal = 23 ÷ 0.144
principal = $159.72 (rounded to the nearest cent)
Therefore, Edwin deposited $159.72 into the savings account.
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Assume all lines that appear parallel, are parallel. Solve for x.
Answer:
[tex] \frac{6}{14} = \frac{x + 6}{4x + 4} [/tex]
[tex]6(4x + 4) = 14(x + 6)[/tex]
[tex]24x + 24 = 14x + 84[/tex]
[tex]10x = 60[/tex]
[tex]x = 6[/tex]
Question 4(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 8x + 64 using a common factor.
O8x(x + 64)
8x(x + 8)
O 8(x+64)
8(x + 8)
Answer:
D
Step-by-step explanation:
Common factor is 8 so 8(x+8) = 8x+64
a circle is centered on point B points A C and d lie on its circumference if angle adc measures 20°, what does angle ABC measure
The measure of the angle ABC, when A, B and C lie on circumference is 40 degrees,
Given that,
Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it
the center of the circle is point 'B'.
three points 'A', 'C', and 'D' lies on the circumference of the
circle.
And angle ADC = 20°.
So, the angle ABC = 40°.
Because the angle made from the center of the circle is twice
the angle made by the three points on the circumference
from the same base.
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a researcher measures the weight of people in a study involving obesity and type 2 diabetes. what type of measurement is being employed?
The valuable insights into complex phenomena like obesity and type 2 diabetes.
The measurement being employed in this scenario is quantitative measurement. Specifically, the researcher is measuring the weight of individuals, which is a numerical value that can be quantified and analyzed statistically.
Quantitative measurement involves collecting numerical data and using statistical methods to analyze and interpret the results. This type of measurement allows researchers to quantify variables and identify patterns, trends, and relationships between different variables.
In the context of this study on obesity and type 2 diabetes, measuring weight is a crucial component of understanding the relationship between these two variables. By collecting weight data from individuals with these conditions, the researcher can analyze the data to determine if there is a correlation between weight and the likelihood of developing type 2 diabetes.
Overall, quantitative measurement is an important tool for researchers in many different fields. It allows them to collect objective data and use statistical methods to analyze and interpret the results, providing valuable insights into complex phenomena like obesity and type 2 diabetes.
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DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!
Here is a graph of f given by f(Θ) = tan(Θ). What are the Θ-intercepts of the graph of f? Explain how you know.
the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.
What area the Θ-intercepts of the graph of f?The Θ-intercepts of a graph of a function f are the values of Θ where the graph intersects the Θ-axis, i.e., where f(Θ) = 0.
In the case of f(Θ) = tan(Θ), we know that the function has vertical asymptotes at Θ = π/2, 3π/2, etc., where the function is undefined. Therefore, the graph of f will intersect the Θ-axis at these values of Θ, since the function is negative for Θ between π/2 and 3π/2 and positive for Θ outside of that interval.
Thus, the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.
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!!!100!!! POINTS PLS HELP AND THANK YOU
What is the average rate of change for the function h(x) = -5x2 + 12x over the interval 2 ≤ x ≤ 5?
-69
-23
23
69
the average rate of change of the function h(x) over the interval 2 ≤ x ≤ 5 is -23. The answer is B) -23.
help please I don’t get this question
The inequality that is true for all values of x is:
√(4x²) ≤ 4x²
Which of the inequalities is true for all values of x?Let's try to find which inequality is true for all real values of x.
For example, let's look at option C, here we have the inequality:
4(x² - 3) ≤ 3(x² - 4)
Let's expand both sides to get:
4x² - 12 ≤ 3x² - 12
4x² ≤ 3x²
4 ≤3
We removed the x-variable, but 4 is not smaller or equal to 3, so this is false.
Now option D, we have:
√(4x²) ≤ 4x²
Notice that bout outcomes are always positive, but in the left side we have a square root.
We can simplify this to get:
2x ≤ 4x²
x ≤ 2x²
This is trivially true, the only region where we can have problems is the region between 0 and 1, but the factor corrects that.
So this one is the correct option.
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a box with a square base and no top is to be built with a volume of 6912 6912 in3 3 . find the dimensions of the box that requires the least amount of material. how much material is required at the minimum?
The box requires a minimum of 4032 square inches of material.
Let's assume that the square base of the box has side length 'x', and the height of the box is 'h'. Then the volume of the box is
V = x^2 × h = 6912
We need to find the dimensions of the box that require the least amount of material. This means we need to minimize the surface area of the box. The surface area of the box is given by
S = x^2 + 4xh
We can solve for 'h' in terms of 'x' using the volume equation
h = 6912 / x^2
Substituting this expression for 'h' into the surface area equation, we get
S = x^2 + 4x(6912/x^2)
Simplifying and taking the derivative of 'S' with respect to 'x', we get
dS/dx = 2x - 27744/x^3
Setting this derivative equal to zero to find the critical points
2x - 27744/x^3 = 0
Multiplying both sides by x^3 and solving for 'x', we get
x = (27744/2)^(1/4) = 18
To confirm that this is a minimum, we need to check the second derivative of 'S' with respect to 'x'
d^2S/dx^2 = 2 + 83208/x^4
At x = 18, we have
d^2S/dx^2 = 2 + 83208/18^4 > 0
Therefore, the critical point at x = 18 corresponds to a minimum surface area.
So the dimensions of the box with the least amount of material are
The side length of the base is 18 inches, and
The height of the box is h = 6912 / 18^2 = 32 inches.
The minimum amount of material required is the surface area of the box, which is
S = 18^2 + 4(18)(32) = 1728 + 2304 = 4032 in^2.
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factor the quadratic
add parentheses to make true.
Answer: 4 x (7+5) = 48
8 . (5-3) . 4 = 64
Step-by-step explanation:
in a distribution for which the mean is 25 and the standard deviation is 5, what percentage of all scores occur at 30 or below?
Step-by-step explanation:
30 is 5 below the mean of 25
this is ONE standard deviation BELOW the mean ( the standard deviation is given as 5)
this represents a Z -score of -1
From Z-score table this represents .1587 of the sample or 15.87 %
The percentage of all scores that occur at 30 or below in a distribution with a mean of 25 and a standard deviation of 5 is 84.13%.
To find the percentage of all scores that occur at 30 or below, we need to calculate the z-score first. The z-score formula is (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.
So, for x = 30, μ = 25, and σ = 5, the z-score is calculated as (30 - 25) / 5 = 1.
We can then use a standard normal distribution table or a calculator to find the proportion of the area under the curve to the left of z = 1. This gives us the percentage of all scores that occur at 30 or below.
Using a standard normal distribution table, we find that the proportion of the area under the curve to the left of z = 1 is 0.8413.
Therefore, the percentage of all scores that occur at 30 or below in this distribution is 84.13%.
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What is 3 and 3 over 5 times 2 and 1 over 4? hurry
Answer:81/20 or 4 1/20
Step-by-step explanation:
To solve this problem, we need to use the rules of multiplication and fractions.
First, we need to convert the mixed numbers to improper fractions:
3 and 3/5 = (5 * 3 + 3) / 5 = 18/5
2 and 1/4 = (4 * 2 + 1) / 4 = 9/4
Now we can multiply the two fractions:
(18/5) * (9/4)
To simplify this expression, we can cancel out any common factors between the numerators and denominators:
(18/5) * (9/4) = (2 * 9)/(5 * 2) * (9/4) = 9/5 * 9/4
Then, we can multiply the numerators and denominators separately:
9/5 * 9/4 = (9 * 9) / (5 * 4) = 81/20
Therefore, 3 and 3/5 times 2 and 1/4 is equal to 81/20 or 4 1/20 as a mixed number.
Answer:
Step-by-step explanation:
[tex]\\8 \frac{1}{10}[/tex]
OW
7 Three clues are shared below. Use the clues
to determine the missing measurement.
Clue #1: this shape has four sides, one set is
parallel
Clue #2: the area measures 40 meter squared
Clue #3: the height is 4 meters
Clue #4: the shorter length is 6 meters
According to the given information the missing measurement is the longer length or base of the parallelogram, which measures 10 meters.
What is meant by parallelogram?A parallelogram is a four-sided geometric shape with two pairs of parallel sides. The opposite sides of a parallelogram have equal lengths and are parallel to each other. The opposite angles of a parallelogram are also equal.
According to the given information:Based on the clues provided, we can determine that the missing measurement is the longer length of the shape. Here's how we can calculate it:
Clue #1 tells us that the shape has four sides, with one set being parallel. This means that the shape is a parallelogram.
Clue #2 tells us that the area of the parallelogram is 40 square meters.
Clue #3 tells us that the height of the parallelogram is 4 meters.
Clue #4 tells us that one of the lengths of the parallelogram is 6 meters.
To find the missing measurement, we can use the formula for the area of a parallelogram:
Area = base x height
Since we know the area and height, we can plug those values in:
40 = base x 4
Solving for the base, we get:
base = 40 / 4 = 10
So the missing measurement is the longer length or base of the parallelogram, which measures 10 meters.
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Over the summer, Naomi and her grandfather built a complex maze for marbles to roll through and shoot out the bottom. When the project was done, Naomi's grandfather surprised her with a tin of 160 beautiful marbles. To see what kinds of marbles were in the tin, Naomi grabbed a handful and got 3 agate, 1 twist, 2 stripe, 1 constellation, and 3 clear marbles.
Based on the data, estimate how many agate marbles are in the tin.
If necessary, round your answer to the nearest whole number.
will give brainlist
Answer:
approximately 48 agate marbles in the tin.
Step-by-step explanation:
Out of the 10 marbles Naomi picked, 3 are agate. We can use this ratio to estimate the number of agate marbles in the tin.
If we assume that the distribution of marbles in the tin is similar to the distribution in the sample of 10 marbles, we can set up a proportion to estimate the number of agate marbles:
3/10 = x/160
Where x is the estimated number of agate marbles in the tin.
Solving for x, we can cross-multiply and get:
3 * 160 = 10 * x
x = 48
we estimate that there are approximately 48 agate marbles in the tin.
14.
6cm
9cm
4cm
3cm
Heh
Answer:
Step-by-step explanation:
its 45 cm due too
Use the information given to determine cos 2x.
sin x = -0.1
Round your answer to three decimal places.
0.98
When you see this kind of problem, try to see how cos 2x and sin x relate--don't go straight to finding x because it is unnecessary. In this case, there is a formula that shows the relationship between cos 2x and sin x as shown:
cos 2x = 1 - 2(sin x)^2
All we have to do is plug in the value of sin x to find the value of cos 2x.
cos 2x = 1 - 2(-0.1)^2 = 1 - 2(0.01) = 1 - 0.02 = 0.98
Answer this I need help?
The weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.
What is y-intercept and slope?The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. whereas there is a net change in the x coordinate, the y coordinate changes just little.
Given the modeled equation for puppy's growth is 2x - y = -2.
The standard equation of line is y = mx + c.
Converting the given model in standard form we have:
2x - y = -2
-y = - 2x - 2
y = 2x + 2
From the equation we see that the y-intercept is 2 and slope is 2.
The graph that has the y-intercept at 2 and slope of 2 is graph H.
Hence, the weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.
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A website has 100,000 members. The number y of members increases by 12% each year.
Identify the exponential function that represents the membership after t years.
WILL GIVE BRAINLIEST
Answer:
The exponential function that represents the membership after t years is given by:
y(t) = 100,000(1 + r)^t
where r is the annual growth rate as a decimal, which is equal to 0.12 in this case.
So the correct answer is:
A. y(t) = 100,000(1 + 0.12)^t
Note that the other options have incorrect expressions for the growth rate and/or the exponent.