Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.4 - Exponential Functions - 1.4 Exercises - Page 54: 32

Answer

a) $0.125\thinspace g$ b) $m=2(\frac{1}{2})^{\frac{1}{15}t}$ c) $0.024\thinspace g$ d) $114.66\thinspace hours$

Work Step by Step

a) We start with 2 grams after 0 hours. After 15 hours, we have 1 gram. After 30 hours, we have 0.5 grams. After 45 hours, we have 0.25 grams. After 60 hours, we have 0.125 grams. b) We start with 2 grams and halve it every 15 hours, so the equation is $m=2(\frac{1}{2})^{\frac{t}{15}}$. c) 4 days = 96 hours. Plug this into $t$ in part (b) to get $\approx 0.024\thinspace grams$. d) Graph the equation in part (b) and $y=0.01$. Find the point where they intersect, which is $(114.66, 0.01)$. The answer is 114.66 hours.
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