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 342: 24

Answer

(a) $m(0)=13kg$ (b) $m(45)\approx6.62kg$

Work Step by Step

So, we have a function of $m(t)=13e^{-0.015t}$, where $t$ stands for days passed and $m(t)$ the amount of mass ($kilograms$) remaining after $t$ days. (a) The mass when $t=0$ (Which means that the substance hasn't started decaying yet) is: $m(0)=13e^0=13\times1=13 kg$ (b) When $t=45$ $m(45)=13e^{-0.015\times45}=13e^{-0.675}\approx6.62kg$
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