Question

Given the equation 1/4(2)^x find the average rate of change between f(2) and f(5)

Answer 1

Given the function


`f(x)=(1)/(4)\,2^(x)`

The average rate between
`f(2)` and
`f(5)` is


`\left.(\Delta f)/(\Delta x)\right|_(x=2\to 5)=(f(5)-f(2))/(5-2)\\ \\ \\ =((1)/(4)\cdot 2^(5)-(1)/(4)\cdot 2^(2))/(5-2)\\ \\ \\ =((1)/(4)\cdot (2^(5)-2^(2)))/(3)\\ \\ \\ =((1)/(4)\cdot (32-4))/(3)\\ \\ \\ =((1)/(4)\cdot (28))/(3)\\ \\ \\ =(7)/(3)`