Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 343: 31

Answer

$A(1)\approx\$7213.18$ $A(2)\approx\$7432.86$ $A(3)\approx\$7659.22$ $A(4)\approx\$7892.48$ $A(5)\approx\$8132.84$ $A(6)\approx\$8380.52$

Work Step by Step

*For a quick review* For Continuously Compounded Interest we have the following formula (Also explained in this chapter, 4.2): $A(t)=Pe^{rt}$ $t$ - number of years $r$ - interest rate per year $P$ - principal $A(t)$ - amount of money after $t$ years --- We have an investment of $\$7000$ and $r=3\%=0.03$, so the formula will get the following form: $A(t)=7000e^{0.03t}$ $A(1)=7000e^{0.03\times1}=7000e^{0.03}\approx\$7213.18$ $A(2)=7000e^{0.03\times2}=7000e^{0.06}\approx\$7432.86$ $A(3)=7000e^{0.03\times3}=7000e^{0.09}\approx\$7659.22$ $A(4)=7000e^{0.03\times4}=7000e^{0.12}\approx\$7892.48$ $A(5)=7000e^{0.03\times5}=7000e^{0.15}\approx\$8132.84$ $A(6)=7000e^{0.03\times6}=7000e^{0.18}\approx\$8380.52$
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