Suppose you turn off the engine of your car when the temperature of the engine reaches 188 °F. If the outside temperature is a constant 63 °F, then the temperature T of the engine t minutes after you turn off the engine satisfies the equation below. = -0.07t In(263) (a) Solve the equation for T. (b) Find the temperature of the engine 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree. of (c) Find T (t) = (d) Find the rate at which the temperature of the engine is changing 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree. °F per minute

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.2: Applied Problems
Problem 37E
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Suppose you turn off the engine of your car when the temperature of the engine reaches 188 °F. If the outside temperature is a constant 63 °F, then the temperature 7 of the engine t minutes after you turn off the engine satisfies the equation below.
T-63
In(26)-
125
(a) Solve the equation for T.
T =
= -0.07t
(b) Find the temperature of the engine 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree.
°F
(c) Find T '(t)
=
(d) Find the rate at which the temperature of the engine is changing 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree.
°F per minute
Transcribed Image Text:Suppose you turn off the engine of your car when the temperature of the engine reaches 188 °F. If the outside temperature is a constant 63 °F, then the temperature 7 of the engine t minutes after you turn off the engine satisfies the equation below. T-63 In(26)- 125 (a) Solve the equation for T. T = = -0.07t (b) Find the temperature of the engine 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree. °F (c) Find T '(t) = (d) Find the rate at which the temperature of the engine is changing 24 minutes after you turn it off. Give your answer to the nearest tenth of a degree. °F per minute
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