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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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Population growth The growth rate of the population P of Horry County in South Carolina from 1970 through 2013 can be modeled by

d P d t = 145.52 t + 2002.3 where t is the time in years, with t = 0 corresponding to 1970. The county’s population was 289,650 in 2013. (Source: U.S. Census Bureau)

(a) Find the model for Horry County’s population.

(b) Use the model to predict the population in 2021. Does your answer seem reasonable? Explain your reasoning.

(a)

To determine

To calculate: The model for Horry County’s population whose growth rate of the population P from 1970 through 2013 is dpdt=145.52t+2002.3 where t is the time in years.

Explanation

Given Information:

The provided model for Horry County’s population is dpdt=145.52t+2002.3. The population of the country in 2013 was 289,650.

Formula used:

The simple power rule of integration xndx=xn+1n+1+C.

Calculation:

Consider the provided model for Horry County’s population is dpdt=145.52t+2002.3.

Integrate the provided model, use the simple power rule of integration xndx=xn+1n+1+C.

dPdtdt=(145.52t+2002.3)dtP(t)=145.52tdt+2002.3dt=145.52[t1+11+1]+2002.3t+C=72

(b)

To determine

To calculate: The prediction of population in 2021 from the model P(t)=72.76t2+2002.3t+69017.86 and whether the population is reasonable.

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