Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 15

$$\$41906.75$$

We are given $$ R(t)=5000 e^{0.1 t},\ \ \ \ \ T=7, \ \ \ \ \ r=0.05$$ Then \begin{align*} P V&=\int_{0}^{7} 5000 e^{0.05 t} d t\\ &=\left.\frac{5000}{0.05} e^{0.05 t}\right|_{0} ^{7}\\ &=100000\left(e^{0.35}-e^{0}\right)\\ & \approx \$41906.75 \end{align*}