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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The water level, measured in feet above mean sea level, of Lake Lanier in Georgia, USA, during 2012 can be modeled by the function

L ( t ) = 0.01441 t 3 0.4177 t 2 + 2.703 t + 1060.1

where t is measured in months since January 1, 2012. Estimate when the water level was highest during 2012.

To determine

To estimate: When the water level was highest during 2012 .

Explanation

Given:

The function of the water level measured in feet above mean sea level, of Lake Lanier in Georgia, USA, is,

L(t)=0.01441t30.4177t2+2.703t+1060.1 ,

where t is measured in months from January 2012.

Calculation:

Consider an initial stage as zero.

Since the process duration is 12 months, the process interval will be [0,12] .

L(t)=0.01441t30.4177t2+2.703t+1060.1

Obtain the first derivative of the function L(t) .

L(t)=3×0.01441t22×0.4177t+2.703=0.04323t20.8354t+2.703

Solve for t by using the quadratic formula.

t=b±b24ac2a=0.8354±0.69794×0.04323×2.7032×0.4323=0.8354±0.23050.08646t=15.33; t=4.11

The critical point values are 15.33 and 4.11.

Notice that the point 15

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