Chapter 7.7, Problem 13PPE

(a)

To determine

Initial amount.

Answer to Problem 13PPE

Initial amount of a is 15,000.

Explanation of Solution

Given data:

Number of student enrolled at a college is 15,000

Growth rate is 4%.

Calculation:

As the number of students enrolled is 15,000 so the initial value will be 15000.

Conclusion:

Initial amount of a is 15,000.

(b)

To determine

Growth factor.

Answer to Problem 13PPE

The growth factor is 1+0.04.

Explanation of Solution

Given data:

Number of student enrolled at a college is 15,000

Growth rate is 4%.

Calculation:

As the present rate of change is $4\%=0.04$

So the growth factor is:

  $\begin{array}{l}1+b\\ b=0.04\\ 1+0.04\end{array}$

Conclusion:

The growth factor is 1.04.

(c)

To determine

Number of student after one year.

Answer to Problem 13PPE

Number of student after one year $15000\cdot 1.04$

Explanation of Solution

Given data:

Number of student enrolled at a college is 15,000

Growth rate is 4%.

Calculation:

Number of student after 1 year:

  $15000\cdot 1.04$

Conclusion:

Number of student after one year $15000\cdot 1.04$

(d)

To determine

Number of students after x years.

Answer to Problem 13PPE

The equation is $15000{(1.04)}^x$

Explanation of Solution

Given data:

Number of student enrolled at a college is 15,000

Growth rate is 4%.

Formula used:

Number of student in x year:

  $y=a(b^x)$

Calculation:

As the starting number $a=15000$

And growth rate $b=1.04$

So the equation will be:

  $15000{(1.04)}^x$

Conclusion:

The equation is $15000{(1.04)}^x$

(e)

To determine

Number of students after 25 yrs.

Answer to Problem 13PPE

Number of students after 25 yrs is 39,988.

Explanation of Solution

Given data:

  $\begin{array}{l}a=15000\\ b=1.04\\ x=25yrs\end{array}$

Formula used:

  $y=a(b^x)$

Calculation:

Number of students after 25 yrs:

  $\begin{array}{l}$ 15000{(1.04)}^x$$ 15000{(1.04)}^{25}$15000(2.66)\\ 39988(approx)\end{array}$

Conclusion:

Number of students after 25 yrs is 39,988.