Question

What is the average rate of change of the function f(x)=480(0.3)x from x = 1 to x = 5?

Answer 1

The rate of change of the function is -35.7

Step-by-step explanation:

The rate of change of a function $f(x)$ between two points $x_1$ and $x_2$ is given by the ratio between the increment of the function itself and the increment of the x-variable:

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

The function of this problem is

$f(x)=480 (0.3)^x$

For $x_1=1$, the value of the function is

$f(1)=480(0.3)^1=144$

For $x_2=5$, the value of the function is

$f(5)=480(0.3)^5=1.2$

Therefore, the rate of change of the function is

$m=\frac{f(5)-f(1)}{5-1}=\frac{1.2-144}{5-1}=-35.7$

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