Q67. - Algebra 2

Question

BUSINESS 

Becca is writing a computer program to find the salaries of her

employees after their annual raise. The percent of increase is represented by p.

Marty’s salary is $\$\mathbf{23},\mathbf{450}$ now. Write a polynomial to represent Marty’s salary

after one year and another to represent Marty’s salary after three years. Assume

that the rate of increase will be the same for each of the three years.

Step-by-Step Solution

Answer

The salary after one year is $(23,450)(p+1)$ and after three years is $(23,450){(p+1)}^3$

Step 1. Given information

Current salary is given as $\$23,450$

Step 2. Concept used

Here $p$ is the annual rate at which salary increasing. So, for finding the amount of salary after number of years, we should multiply the salary by $p$ of the previous year and add the previous year salary to get the current salary.

Step 3. Calculation

Salary of Marty after one year,

Multiply by and add salary as,

 $\begin{array}{l}=(23,450)\left(p\right)+23,450\\ =(23,450)(p+1)\end{array}$

Salary after two years,

 $\begin{array}{l}=(23,450)(p+1)+(23,450)(p+1)p\\ =(23,450)(p+1)(p+1)\\ =(23,450)2\end{array}$

Similarly,

Salary after three years,