Chapter 9.7, Problem 4PPS

(a)

To determine

An equation for the number of memberships sold at work-out-gym t years after 2001

Answer to Problem 4PPS

The equation for the number of memberships sold at work-out-gym t years after 2001 $A=550{\left(1.03\right)}^t$

Explanation of Solution

Given information:

The work-out-gym sold 550 memberships in 2001 and rate 3% annually

So the value is

  $\begin{array}{c}P=550\\ t=t\\ r=3\%\\ =\frac{3}{100}\\ =0.03\\ n=1\end{array}$

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 number of memberships sold at work-out-gym t years after 2001 is as below:

  $\begin{array}{c}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =550{\left(1+\frac{0.03}{1}\right)}^t\\ A=550{\left(1.03\right)}^t\end{array}$

Thus, the equation for the number of memberships sold at work-out-gym t years after 2001 $A=550{\left(1.03\right)}^t$

(b)

To determine

How many memberships the gym will sent in 2020

Answer to Problem 4PPS

The gym will sent $852$

Explanation of Solution

Given information:

The work-out-gym sold 550 memberships in 2001 and rate 3% annually

So the value is

  $\begin{array}{l}A=550{\left(1.03\right)}^t\\ t=19\end{array}$

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:

  $\begin{array}{c}A=550{\left(1.03\right)}^t\\ A=550{\left(1.03\right)}^{15}\\ =550\times 1.55\\ A=852\end{array}$

Thus, the gym will sent $852$