Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 489: 103

Answer

$ a.\quad 37.3$ million $ b.\quad $ in 2017.

Work Step by Step

$ a.$ In the year 2010, t is 0. Substitute 0 for t in the formula and calculate. $ A=37.3e^{0}$ = $37.3$ million. $ b.$ Solve for t when $ A=40$ $ 40=37.3 e^{0.0095t}\quad $ ... $/\div 37.3$ $\displaystyle \frac{40}{37.3}=e^{0.0095t}\quad $ ... $/\ln(...)$ $\displaystyle \ln(\frac{40}{37.3})=0.0095t\quad $ ... $/\div 0.0095$ $ t=\displaystyle \frac{\ln(\frac{40}{37.3})}{0.0095}\approx 7.356$ (years after 2010) The population will reach 40 million in 2017.
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