![R= 2.6](/tpl/images/0992/3835/b9794.png)
Step-by-step explanation:
Given
![f(x) = 40e^{.06t](/tpl/images/0992/3835/2152d.png)
![[a,b] = [0,3]](/tpl/images/0992/3835/bc84d.png)
Required
Determine the average rate of change (R)
This is calculated as follows:
![R = \frac{f(b) - f(a)}{b - a}](/tpl/images/0992/3835/9fb4c.png)
Where
and ![b = 3](/tpl/images/0992/3835/27574.png)
Substitute 0 for a and 3 for b
![R = \frac{f(3) - f(0)}{3 - 0}](/tpl/images/0992/3835/766b1.png)
![R = \frac{f(3) - f(0)}{3}](/tpl/images/0992/3835/25da5.png)
![R = \frac{1}{3}[f(3) - f(0)]](/tpl/images/0992/3835/a5854.png)
Calculate f(3)
![f(x) = 40e^{.06t](/tpl/images/0992/3835/2152d.png)
![f(3) = 40e^{.06*3}](/tpl/images/0992/3835/679be.png)
![f(3) = 40e^{0.18}](/tpl/images/0992/3835/b56eb.png)
![f(3) = 40 * 1.197](/tpl/images/0992/3835/46beb.png)
![f(3) = 47.88](/tpl/images/0992/3835/f2e08.png)
Calculate f(0)
![f(x) = 40e^{.06t](/tpl/images/0992/3835/2152d.png)
![f(0) = 40e^{.06*0}](/tpl/images/0992/3835/178f7.png)
![f(0) = 40e^{0}](/tpl/images/0992/3835/5cbfc.png)
![f(0) = 40*1](/tpl/images/0992/3835/34ef7.png)
![f(0) = 40](/tpl/images/0992/3835/30a6a.png)
So, the expression:
![R= \frac{1}{3}[47.88 - 40]](/tpl/images/0992/3835/044aa.png)
![R= \frac{1}{3}[7.88]](/tpl/images/0992/3835/a4c05.png)
![R= 2.62666666667](/tpl/images/0992/3835/3ac02.png)
![R= 2.6](/tpl/images/0992/3835/b9794.png)
Hence, the average rate of change is approximately 2.6