Answered: In the morning, a cup of hot coffee hot…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Related questions

Question

In the morning, a cup of hot coffee hot coffee is 210 degrees Fahrenheit and the kitchen where the coffee was sitting temperature is 78 degrees Fahrenheit. 1 minute later a sip is taken and the temperature of the coffee at this point is 200 degrees Fahrenheit.

If I like to drink my coffee when it is 170 degrees Fahrenheit, how long must I wait? Please answer in minutes and seconds!

Expert Solution

Step 1

Given that a cup of hot coffee is $210$ degrees Fahrenheit and the kitchen where the coffee was sitting temperature is $78$ degrees Fahrenheit.

Find if the coffee is drink when it is $170$ degrees Fahrenheit, how long must wait.

Newton's law of cooling states that the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.

That is $T (t) = T_{s} + (T_{0} - T_{s}) e^{- kt}$

where $t$ is the time, $T (t)$ be the temperature of the given body at time $t$ , $T_{s}$ be the surrounding temperature, $T_{0}$ be the initial temperature of the body and $k$ is the constant.