What is the average rate of change of the function f(x)=20(14)xf(x)=20(14)x from x = 1 to x = 2? Enter your answer, as a decimal, in the box. Do not round your answer.

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= 2At x = 1then;[tex]f(x) = 20 \cdot(\frac{1}{4})^1 = 5[/tex]At x = 2then;[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