## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 14

#### Answer

$$\3296.8$$

#### Work Step by Step

W are given$$R(t)=800,\ \ \ \ \ T=5, \ \ \ \ \ r=0.08$$ Then \begin{align*} P V&=\int_{0}^{T} R(t) e^{-r t} d t\\ &= \int_{0}^{5} 800 e^{-0.08 t} d t\\ &=\left.\frac{800}{-0.08} e^{-0.08 t}\right|_{0} ^{5}\\ &=-10000\left(e^{-0.4}-e^{0}\right)\\ & \approx \\$3296.8 \end{align*}

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