a. Answer y = 20 Explanation Given information: An object at a temperature of 160 ° C was removed from a furnace and placed in a room at 20 ° C . Table shows the measured data and model for data is, T = 20 + 140 e − 0.68 h H o u r s ( h ) T e m p e r a t u r e , ( T ) 0 160 ° 1 90 ° 2 56 ° 3 38 ° 4 29 ° 5 24 ° Graph of table data is also given. Calculation: Consider the model, T = 20 + 140 e − 0.68 h To identify the horizontal asymptote of the model using graph, draw a line parallel to x − a x i s as the time approaches infinity. Now identify y − int e r c e p t of on the graph by parallel line, which is 20 Hence the horizontal asymptote of the model is y = 20 b. To determine Use the model to approximate the object time for temperature 100°C. Answer 0.81 h o u r s Explanation Given information: An object at a temperature of 160 ° C was removed from a furnace and placed in a room at 20 ° C . Table shows the measured data and model for data is, T = 20 + 140 e − 0.68 h H o u r s ( h ) T e m p e r a t u r e , ( T ) 0 160 ° 1 90 ° 2 56 ° 3 38 ° 4 29 ° 5 24 ° Calculation: Consider the model, T = 20 + 140 e − 0.68 h o r T = 20 [ 1 + 7 ( 2 − h ) ] p u t T = 100 100 = 20 [ 1 + 7 ( 2 − h ) ] 5 = [ 1 + 7 ( 2 − h ) ] 4 = 7 ( 2 − h ) 2 − h = 4 / 7 2 − h = 0.5714 A p p l y log b o t h s i d e s ln 2 − h = ln 0.5714 − h ln 2 = ln 0.5714 h = − ln 0.5714 ln 2 h = 0.81 Hence, the object time for temperature 100°C, after taken out from furnace is 0.81 h o u r s

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.4, Problem 88E

To determine

Use the graph to identify the horizontal asymptote of the model.

Expert Solution

Answer to Problem 88E

y=20

Explanation of Solution

Given information:

An object at a temperature of 160°C was removed from a furnace and placed in a room at 20°C .

Table shows the measured data and model for data is,

T=20+140e−0.68h

Hours (h)Temperature, (T)0160°190°256°338°429°524°

Graph of table data is also given.

EBK PRECALCULUS W/LIMITS, Chapter 3.4, Problem 88E , additional homework tip 1

Calculation:

Consider the model,

T=20+140e−0.68h

To identify the horizontal asymptote of the model using graph, draw a line parallel to x−axis as the time approaches infinity.

EBK PRECALCULUS W/LIMITS, Chapter 3.4, Problem 88E , additional homework tip 2

Now identify y−intercept of on the graph by parallel line, which is 20

Hence the horizontal asymptote of the model is y=20

To determine

Use the model to approximate the object time for temperature 100°C.

Expert Solution

Answer to Problem 88E

0.81 hours

Explanation of Solution

Given information:

An object at a temperature of 160°C was removed from a furnace and placed in a room at 20°C .

Table shows the measured data and model for data is,

T=20+140e−0.68h

Hours (h)Temperature, (T)0160°190°256°338°429°524°

Calculation:

Consider the model,

T=20+140e−0.68horT=20[1+7(2−h)]put T=100100=20[1+7(2−h)]5=[1+7(2−h)]4=7(2−h)2−h=4/72−h=0.5714Apply log both sidesln2−h=ln0.5714−hln2=ln0.5714h=−ln0.5714ln2h=0.81

Hence, the object time for temperature 100°C, after taken out from furnace is 0.81 hours

Chapter 3.4, Problem 87E

Chapter 3.4, Problem 89E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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