Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.6 - Modeling with Exponential Functions - 4.6 Exercises - Page 380: 28

Answer

$57^\circ C$ see graph.

Work Step by Step

Use the Newton's Law of Cooling $T(t)=T_s+D_0e^{-kt}$ with the given conditions $T_s=20, D_0=100-20=80,T(15)=75$, we have $75=20+80e^{-15k}$ which gives $k=-ln(\frac{75-20}{80})/15\approx0.0313$ thus the equation becomes $T(t)=20+80e^{-0.0313t}$ which can be graphed and shown in the figure. After another 10 minutes $t=25$ and $T(25)=20+80e^{-0.0313\times25}\approx57^\circ C$
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