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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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Modeling Exponential Growth and Decay In Exercises 119 and 120, find the exponential function y = C e k t that passes through the two given points.

( 1 , 1 ) , ( 5 , 5 )

To determine

To calculate: The exponential function y=Cekt passing through the points (1,1),(5,5).

Explanation

Given Information:

The provided points are (1,1),(5,5).

Formula used:

Formula for ln is:

ln(x)n=nln(x)

And lne=1

Calculation:

Consider the exponential function y=Cekt passing through the points (1,1),(5,5)

As the exponential function passes through the points (1,1),(5,5).

Hence the points (1,1),(5,5) satisfy the equation of exponential function y=Cekt.

Substitute t=1,y=1 in the equation y=Cekt:

1=Cek(1)1=Cek

Substitute t=5,y=5 in the equation y=Cekt:

5=Cek(5)5=Ce5k

Now, take the ratio of the equations Cek=1 and <

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