# To represent the population of a planned seaside community in Florida for the given function p ( t ) = 3000 + 200 t + 0.1 t 2 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 59RE

a.

To determine

## To represent the population of a planned seaside community in Florida for the given function   p(t)=3000+200t+0.1t2 .

Expert Solution

The population of a planned seaside community in Florida of the given function for t=10   is 5010 and t=20 is 7040 .

### Explanation of Solution

Given information: Consider the function, p(t)=3000+200t+0.1t2

Calculation:

p(10)=3000+200(10)+0.1(10)2=300+2000+0.1(100)=5000+10=5010p(10)=5010Now,p(20)=3000+200(20)+0.1(20)2=3000+4000+0.1(400)=3000+4000+40=7040

The value 5010 and 7040 represent the population in 1995 and 2005 respectively.

b.

To determine

### To find the average rate of change of P between t=10   and t=20 , also representation of the numbers.

Expert Solution

The average rate of change of P between t=10   and t=20 is 203 and this represents average annual population increase.

### Explanation of Solution

Given information: Consider the function, p(t)=3000+200t+0.1t2

Calculation:

Since the population in 1995 was 5010 and in 2005 is 7040 , so in 10 years the difference of the population is

p(20)p(10)=70405010=2030

So, the average range of change of p between t=10 and t=20 will be,203010=203

Hence 203 people/year is the average range of change and this represents average annual population increase.

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