Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 4 - Exponential Functions - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 146: 37

Answer

$Y(t)=300- 300\cdot (0.97)^t$

Work Step by Step

The problem describes an exponential function with the following parameters. \begin{equation} \begin{aligned} a&= 300\\ r&= 3\%= 0.03\\ b&=1-r = 0.97 \end{aligned} \end{equation} Note that the yam's temperature is the difference between the oven's initial temperature and the temperature difference between the oven and the yam's temperature. Hence, a model of the yam's temperature is \begin{equation} \begin{aligned} Y(t)&=a-a\cdot b^t\\ &=300- 300\cdot (0.97)^t\\ \end{aligned} \end{equation}
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