## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 5 - 5.5 - Exponential and Logarithmic Models - 5.5 Exercises - Page 405: 26

#### Answer

$y= \dfrac{1}{2} e^{\frac{x}{4}\ln 10}$

#### Work Step by Step

We have $y=ae^{bx}$ Set $(x,y)= (0, \dfrac{1}{2})$ So, $\dfrac{1}{2}=ae^{b(0)} \implies a=\dfrac{1}{2}$ Further, we have $y=ae^{bx}$ Set $(x,y)= (4,5)$ to compute $b$ So, $5=\dfrac{1}{2} e^{4b} \implies e^{4b}=10$ and $\ln 10 =\ln 4b \implies b =\dfrac{1}{4} \ln 10$ Now, the exponential decay model is: $y= \dfrac{1}{2} e^{\frac{x}{4}\ln 10}$

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