   Chapter 4.6, Problem 21E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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 , 5 ) ,   ( 12 , 20 )

To determine

To calculate: The exponential models y1=Cek1t and y2=C(2)k2t for the exponential model passing through the points (0,5),(12,20).

Explanation

Given Information:

The provided points are (0,5),(12,20) and the exponential models are y1=Cek1t and y2=C(2)k2t.

Calculation:

Consider the provided points are (0,5),(12,20) and the exponential models are y1=Cek1t and y2=C(2)k2t.

Consider the exponential model y1=Cek1t.

Consider the points (0,5),(12,20).

Substitute t=0,y1=5 in the exponential model y1=Cek1t,

5=Cek105=Ce0C=5

Substitute t=12,y1=20 in the exponential model y1=5ek1t,

20=5ek112e12k1=205e12k1=4

Take natural log on both the sides,

ln (e12k1)=ln 412k1 lne=ln 412k1=ln 4k1=ln 412

Solve further,

k1=0.1155

Substitute k1=0.1155 and C=5 in the exponential model y1=Cek1t,

y1=5e0.1155t

Hence, the exponential model is y1=5e0

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