Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Chapter 6.6, Problem 19E
To determine

To calculate: .The waiting time when you can continue driving.

Expert Solution & Answer
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Answer to Problem 19E

The required time is 50 minute.

Explanation of Solution

Given Information:

Temperature of car overheats is 280F .

Temperature of car driven is 230F .

Temperature of outside is 80F .

Also, cooling rate of car is r=0.0058 .

Formula Used:

Newton’s Law of Cooling:

  T=(T0TR)ert+TR

Where, T0 is initial temperature, T is temperature of the body, TR is surrounding temperature, r is heat transfer coefficient, and t is time.

Power rule of logarithmic functions.

  logaxp=plogax

Where a is the base, x is the variables and p is the power of variables.

Calculation:

Use Newton’s Law of Cooling formula.

  T=(T0TR)ert+TR

Substitute for T0 , 230 for T , 80 for TR and 0.0058 for 0.0058 .

  230=(28080)e(0.0058)t+80

Simplify the above equation.

  230=(28080)e(0.0058)t+80230=200e(0.0058)t+8023080=200e(0.0058)t150=200e(0.0058)t

Simplify the equation.

  150=200e(0.0058)t150200=e(0.0058)t0.75=e(0.0058)t

Take natural logarithm with base e of the above equation.

  lne(0.75)=lnee(0.0058)t

Now, use power rule of logarithm logaxp=plogax in the above equation.

  lne(0.75)=(0.0058t)lnee

Substitute 1 for lnee in the above equations.

  lne(0.75)=(0.0058t)(1)lne(0.75)=(0.0058t)

Substitute 0.2877 for lne(0.75) in the above equation.

  0.2877=(0.0058t)

Simplify the above equation.

  0.2877=(0.0058t)t=0.2877(0.0058)t=49.603t50

Hence, the required time is 50 minutes.

Chapter 6 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - 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