## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 3 - Section 3.5 - Exponential Growth and Decay; Modeling Data - Exercise Set - Page 505: 2

#### Answer

$31.5$ million.

#### Work Step by Step

The mathematical model for exponential growth or decay is given by $f(t)= A_{0}e^{kt}$ or $A= A_{0}e^{kt}$. If $k \gt 0$, the function models the amount of a growing entity. $A_{0}$ is the original amount, or size, of the growing entity at time t = 0, $A$ is the amount at time $t$, and $k$ is a constant representing the growth rate. If k $\lt$ 0, the function models the amount of a decaying entity ---- In 2010, the time passed, t=0 (t = years after 2010), and $A_{0}$ for the given model $\quad A=31.5e^{0.019t}$ equals $31.5$ million.

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