Enrollment in a school has grown exponentially since the school opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 20.

Question

An exponential graph has time in years on the x axis and enrollments on the y axis. An upward rising curve begins at zero comma thirty and passes through twenty comma eighty.

0.4
2.5
5
30

Answer 1

To determine the average rate of change from \( x = 0 \) to \( x = 20 \), we need to apply the formula for the average rate of change, which is:

\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]

where \( f(x) \) is the function representing the enrollment numbers, and \( a \) and \( b \) are the values of \( x \) at the start and end of the interval, respectively.

Given the information:

• At \( x = 0 \) (the year the school opened), the enrollment \( f(0) \) is 30.
• At \( x = 20 \), the enrollment \( f(20) \) is 80.

Now, substituting these values into the formula:

\[ \text{Average Rate of Change} = \frac{f(20) - f(0)}{20 - 0} = \frac{80 - 30}{20 - 0} = \frac{50}{20} = 2.5 \]

Thus, the average rate of change from \( x = 0 \) to \( x = 20 \) is \( \boxed{2.5} \).