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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4.6, Problem 22E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Exponential Models In Exercises 21 and 22, find exponential models y 1 = C e k 1 t  and  y 2 =   C ( 2 ) k 2 t that pass through the two given points. Compare the values of k 1  and  k 2 .

Briefly explain your results.

( 0 , 8 ) ,   ( 20 , 1 2 )

To determine

To calculate: The exponential models y1=Cek1t and y2=C(2)k2t for the exponential model passing through the points (0,8),(20,12).

Explanation

Given Information:

The provided points are (0,8),(20,12) and the exponential models are y1=Cek1t and y2=C(2)k2t.

Calculation:

Consider the provided points are (0,8),(20,12) and the exponential models are y1=Cek1t and y2=C(2)k2t.

Consider the exponential model y1=Cek1t.

Consider the points (0,8),(20,12).

Substitute t=0,y1=8 in the exponential model y1=Cek1t,

8=Cek1⋅08=Ce0C=8

Substitute t=20,y1=12 in the exponential model y1=8ek1t,

12=8ek1⋅20e20k1=116e20k1=116

Take natural log on both the sides,

ln (e20k1)=ln (116)20k1 lne=ln (116)20k1=ln (116)k1=ln (116)20

Solve further,

k1=−0.1386

Substitute k1=−0.1386 and C=8 in the exponential model y1=Cek1t,

y1=8e−0.1386t

Hence, the exponential model is y1=8e−0

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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Research Methods for the Behavioral Sciences (MindTap Course List)

What is the novelty effect, and how does it affect a studys external validity?

Research Methods for the Behavioral Sciences (MindTap Course List)

Refer to exercise 7, where an estimated regression equation relating years of experience and annual sales was d...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A Pew Research Center survey asked adults if their ideal place to live would have a faster pace of life or a sl...

Statistics for Business & Economics, Revised (MindTap Course List)

The following Exercises 22 through 27 involve circles and sectors. Where necessary, round the answer to 1 decim...

Mathematics For Machine Technology

Finding a Maclaurin Series In Exercises 27-40, find the Maclaurin series for the function. Use the table of pow...

Calculus (MindTap Course List)

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