Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 13

$$PV= \$39346.93$$

We are given: $$R(t)=5000, \ \ \ \ T=10,\ \ \ \ r=0.05 $$ Then \begin{align*} P V&=P V=\int_{0}^{T} R(t) e^{-r t} d t\\ &=\int_{0}^{10} 5000 e^{-0.05 t} d t\\ &=\left.\frac{5000}{-0.05} e^{-0.05 t}\right|_{0} ^{10}\\ &=-100000\left(e^{-0.5}-e^{0}\right)\\ & \approx \$ 39346.93 \end{align*}