Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 9 - Section 9.4 - Logistic Functions and Models - Exercises - Page 669: 33a

Answer

$T(t)=\displaystyle \frac{1090}{1+0.412(1.09)^{-t}}$ Level-off value is $N=1090.$

Work Step by Step

(We use desmos.com for the calculations/graph below.) Logistic Model form: $\displaystyle \quad R=\frac{N}{1+Ab^{-t}}$ 1. create a table with variable names $t$ and $T$ and enter the data. 2. in the next free cell, enter $T\sim N/1+Ab^{-t}$ The calculator returns $\left\{\begin{array}{l} N=1090\\ A=0.412\\ b=1.09 \end{array}\right.$ (rounded to 3 significant figures.) $T(t)=\displaystyle \frac{1090}{1+0.412(1.09)^{-t}}$ Level-off value is $N=1090.$
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