Question

Find and interpret the rate of change on the interval. Round your answer to the nearest whole number. (Number 4 at the top)

Answer 1

We are given the function

`\begin{gathered} f(t)=12(1.2)^t \\ on\text{ the interval }[3,6] \end{gathered}`

Step 1: Formula for the Average rate of Change

`AverageRate=(f(b)-f(a))/(b-a)`

Step 2: Identify the parameters

From the question,

`\begin{gathered} a=3 \\ b=6 \\ f(t)=12(1.2)^t \\ f(a)=f(3)=12(1.2)^3=20.736 \\ f(b)=f(6)=12(1.2)^6=35.831808 \end{gathered}`

Step 3: Substituting the parameters

`\begin{gathered} Average\text{ }Rate(A.R)=(f(b)-f(a))/(b-a) \\ \\ A.R=(35.831808-20.736)/(6-3) \\ A.R=5.031936 \\ \\ A.R=5\text{ \lparen to the nearest whole number\rparen} \end{gathered}`

Therefore, the Average Rate = 5 (to the nearest whole number)