Chapter 8 - Further Applications of Integration - 8.4 Applications to Economics and Biology - 8.4 Exercises - Page 613: 16

$\approx 47645$

$$\int_{0}^{T}8000e^{0.04t}\cdot e^{-rt}dt$$ $$\int_{0}^{T}8000e^{0.04t-rt}dt$$ $$8000\int_{0}^{T}e^{0.04t-rt}dt$$ $$8000\int_{0}^{T}e^{(0.04-r)t}dt$$ $$\frac{8000}{0.04-r}[e^{(0.04-r)t}]_{0}^{T}=\frac{8000}{0.04-r}(e^{(0.04-r)T}-e^{(0.04-r)0})=\frac{8000}{0.04-r}(e^{(0.04-r)T}-1)=\frac{8000}{0.04-6.2\%}(e^{(0.04-6.2\%)6}-1)\approx 47645$$