Chapter 9.7, Problem 3CYU

(a)

To determine

An equation for the enrollment of Polaris High School t years after 2000

Answer to Problem 3CYU

The equation for the enrollment of Polaris High School t years after 2000 is $A=88647{\left(1.002\right)}^t$

Explanation of Solution

Given information:

In 2000,2200 students attended Polaris High School and declining rate is 2% annually

So the value is

  $\begin{array}{c}P=2200\\ t=t\\ r=2\%\\ =\frac{2}{100}\\ =0.02\\ n=12\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the equation for the enrollment of Polaris High School t years after 2000 is as below:

  $\begin{array}{c}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =2200{\left(1+\frac{0.02}{12}\right)}^t\\ A=2200{\left(1.002\right)}^t\end{array}$

Thus, the equation for the enrollment of Polaris High School t years after 2000 is $A=2200{\left(1.002\right)}^t$

(b)

To determine

How many students will be enrolled in 2015

Answer to Problem 3CYU

The students will be enrolled in 2015 $A=2266$

Explanation of Solution

Given information:

In 2000,2200 students attended Polaris High School and declining rate is 2% annually

So the value is

  $\begin{array}{l}A=2200{\left(1.002\right)}^t\\ t=15\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the students will be enrolled in 2015 is as below:

  $\begin{array}{c}A=2200{\left(1.002\right)}^t\\ =2200{\left(1.002\right)}^{15}\\ =2200\times 1.030\\ A=2266\end{array}$

Thus, the students will be enrolled in 2015 $A=2266$