Question

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Enrollment at a golf academy has grown exponentially since the academy opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 4.


A) 0.067

B) 4

C) 15

D) 75

Answer 1

Answer:

C

Step-by-step explanation:

The rate of change of a function in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b } = [ 0, 4 ]

From the graph

f(b) = f(4) = 75 and f(a) = f(0) = 15, thus

average rate of change = $\frac{75-15}{4-0}$ = $\frac{60}{4}$ = 15

Answer 2

The average rate of change from x =0 to x = 4 is 15.

The calculation is as follows:

• The rate of change should represent the function in the closed interval (a,b).

i.e.

$\frac{f(b) - f(a)}{b - a}$

• The (a,b) = (0,4).
• Now based on the graph f(b) = f(4) = 75 and f(a) = f(0) = 15.

So,

$= \frac{75-15}{4-0}\\\\= \frac{60}{4}$

= 15

Therefore we can conclude that the average rate of change from x =0 to x = 4 is 15.

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