Solution
We are given the function
[tex]\begin{gathered} f(t)=12(1.2)^t \\ on\text{ the interval }[3,6] \end{gathered}[/tex]Step 1: Formula for the Average rate of Change
[tex]AverageRate=\frac{f(b)-f(a)}{b-a}[/tex]Step 2: Identify the parameters
From the question,
[tex]\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}[/tex]Step 3: Substituting the parameters
[tex]\begin{gathered} Average\text{ }Rate(A.R)=\frac{f(b)-f(a)}{b-a} \\ \\ A.R=\frac{35.831808-20.736}{6-3} \\ A.R=5.031936 \\ \\ A.R=5\text{ \lparen to the nearest whole number\rparen} \end{gathered}[/tex]Therefore, the Average Rate = 5 (to the nearest whole number)