Answer:
Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given the function:
[tex]f(x) = 20 \cdot(\frac{1}{4})^x[/tex]
We have to find the average rate of change from x = 1 to x= 2
At x = 1
then;
[tex]f(x) = 20 \cdot(\frac{1}{4})^1 = 5[/tex]
At x = 2
then;
[tex]f(x) = 20 \cdot(\frac{1}{4})^2=20 \cdot \frac{1}{16} = 1.25[/tex]
Substitute these in above formula we have;
[tex]A(x) = \frac{f(2)-f(1)}{2-1}[/tex]
⇒[tex]A(x) = \frac{1.25-5}{1}=-3.75[/tex]
therefore, average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75
