Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.1 - Exponential Functions - 4.1 Exercises - Page 337: 56

Answer

1% -> 5255.05 dollars 2% -> 5520.40 dollars 3% -> 5796.37 dollars 4% -> 6083.26 dollars 5% -> 6381.41 dollars 6% -> 6691.13 dollars

Work Step by Step

First one has to find the function that models the example. This uses an exponential function and its base is $n\cdot r^t$ where $n$ is the initial value, $r$ is the growth rate, and $t$ is the time in years passed. There is an initial investment of \$5000 dollars, so that corresponds to $n$. The investment asked to calculate is after 5 years, so it corresponds to $t$. Now the function can be described: $f(r)=5000\cdot r^5$ Now one only needs to calculate $f(1.01)$, $f(1.02)$, $f(1.03)$, $f(1.04)$, $f(1.05)$, and $f(1.06)$ which corresponds to the investment for 101%, 102%, 103%, 104%, 105%, and 106% growth rate, respectively.
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