Question

Enrollment in a school has grown exponentially since the school opened. A graph depicting this growth is shown. Determine the percentage rate of growth.

Answer 1

Answer:

4.6%

Step-by-step explanation:

Let the horizontal axis be represented by x and the vertical axis be represented by f(x) or y

The general exponential function is of the form:

$f(x) = a(b)^{x}$

Here,

a = value at the starting of the graph

b = growth factor

In order to find the percentage rate of growth, we need to find the value of b, the growth factor. From the graph we can see two points on the graph: (20, 80) and (25, 100). This means for x = 20, value of f(x) is 80. Using this point in the function equation, we get:

$80 = a(b)^{20}$                             Equation 1

Using the second point (25, 100) in the function equation, we get:

$100 = a(b)^{25}$                             Equation 2

Dividing Equation 2 by Equation 1, we get:

$\frac{100}{80}=\frac{ab^{25}}{ab^{20}}\\\\ 1.25=b^{5}\\\\ b=1.046$

Using the value of b, the function equation becomes:

$f(x) = a(1.046)^{x}$

This means, after every year, the number of enrollments is 1.046 times the previous year. Or in other words, the number of enrollment is 0.046 times more the previous year. This shows the number of enrollments grow by 0.046 every year which is equal to 4.6%

Thus, the percentage rate of growth is 4.6%

Answer 2

Answer:

The answer is 1.06 guys. you just divide the percentage and growth.

Step-by-step explanation: