Chapter 9.6, Problem 33PPS

To determine

How many student will graduate in 2012

Answer to Problem 33PPS

The students will graduate is $198$

Explanation of Solution

Given information:

The number of graduates at a high school increased by a factor of 1.055 every year since 2001 and 110 students graduated and the function $N=110{\left(1.055\right)}^t$

So the value is

  $\begin{array}{c}P=110\\ t=11\\ \left(1+r\right)=1.055\end{array}$

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 how many students will graduate in 2012 is below

  $\begin{array}{c}N=110{\left(1.055\right)}^t\\ t=11\\ N=110{\left(1.055\right)}^{11}\\ =110\left(1.80\right)\\ N=198\end{array}$

Thus, the students will graduate is $198$