Chapter 7.7, Problem 7CYU

a.

To determine

The equation of student enrolling in Polaris High School fort years after 2015.

Answer to Problem 7CYU

The equation of student enrolling in Polaris High School fort years after 2015 $=2200{\left(0.98\right)}^t$

Explanation of Solution

Given:

The number of student attended class in2015 are2200 and the declining rate of enrollment is 2% annually

Concept used:

The formula of reduction rate over a time period is given by,

  $\begin{array}{l}F=A{\left(1-r\right)}^t\\ \text{Here,}A\text{is the number of student in 2015}\\ \text{Here,}F\text{is}\text{the number of student after t years}\\ r\text{is the percentage reduced }\\ \text{t is the years}\end{array}$

Calculation:

The number of student aftert is calculated as,

  $\begin{array}{c}F=2200{\left(1-0.02\right)}^t\\ =2200{\left(0.98\right)}^t\end{array}$

Conclusion:

Hence, the equation of student enrolling in Polaris High School fort years after 2015 $=2200{\left(0.98\right)}^t$

b.

To determine

The number of studentsenrolling in 2030.

Answer to Problem 7CYU

The number of student enroll in 2030 is $1200$

Explanation of Solution

Given:

The number of students attending class in2015 are2200 and the declining rate of enrollment is 2% annually

Concept used:

The formula of reduction rate over a time period is given by,

  $\begin{array}{l}F=A{\left(1-r\right)}^t\\ \text{Here,}A\text{is the number of student in 2015}\\ \text{Here,}F\text{is}\text{the number of student after t years}\\ r\text{is the percentage reduced }\\ \text{t is the years}\end{array}$

Calculation:

The number of student enroll in 2030 is calculated as,

  $\begin{array}{c}F=2200{\left(1-0.02\right)}^t\\ =2200{\left(0.98\right)}^{30}\\ =2200\left(0.5454\right)\\ \approx 1200\end{array}$

Conclusion:

Hence, the number of student enroll in 2030 is $1200$