Chapter 12, Problem 30RE

a.

To determine

To find: a formula for the salary of the teacher.

Answer to Problem 30RE

  $A_n=35000+\left(n-1\right)\cdot 1200$

Explanation of Solution

Given information:

The teacher makes $35000 in the first year and gets a raise of $1200 each year.

Calculation:

If the first-year salary is $A_1$ , then

  $\begin{array}{l}{A}_2=A_1+1200\\ A_3=A_2+1200=A_1+1200+1200=A_1+2\cdot 1200\\ A_4=A_3+1200=A_1+2\cdot 1200+1200=A_1+3\cdot 1200\\ .\\ .\\ .\\ A_n=A_1+\left(n-1\right)\cdot 1200\end{array}$

Since $A_1=35000$ , the formula for his salary in nth year can be given as

  $A_n=35000+\left(n-1\right)\cdot 1200$

Conclusion:

The formula for his salary in the nth year is $A_n=35000+\left(n-1\right)\cdot 1200$

b.

To determine

To list: the salary of the teacher for the first eight years and compare his salary with her colleague.

Answer to Problem 30RE

Her salary for the first 8 years are $\$35000,\$36200,\$37400,\$38600,\$39800,\$40000,\$41200,\$42400$.

Her colleague stats receiving more salary to compare to her from 6^th year.

Explanation of Solution

Given information:

The teacher makes $35000 in the first year and gets a raise of $1200 each year.

Calculation:

The formula for his salary in nth year is $A_n=35000+\left(n-1\right)\cdot 1200$.

So,

  $\begin{array}{l}{A}_1=35000+\left(1-1\right)\cdot 1200=35000+\left(0\right)\cdot 1200=35000\\ A_2=35000+\left(2-1\right)\cdot 1200=35000+\left(1\right)\cdot 1200=36200\\ A_3=35000+\left(3-1\right)\cdot 1200=35000+\left(2\right)\cdot 1200=37400\\ A_4=35000+\left(4-1\right)\cdot 1200=35000+\left(3\right)\cdot 1200=38600\\ A_5=35000+\left(5-1\right)\cdot 1200=35000+\left(4\right)\cdot 1200=39800\\ A_6=35000+\left(6-1\right)\cdot 1200=35000+\left(5\right)\cdot 1200=40000\\ A_7=35000+\left(7-1\right)\cdot 1200=35000+\left(6\right)\cdot 1200=41200\\ A_8=35000+\left(8-1\right)\cdot 1200=35000+\left(8\right)\cdot 1200=42400\end{array}$

Therefore, her salary for the first 8 years are $\$35000,\$36200,\$37400,\$38600,\$39800,\$40000,\$41200,\$42400$.

The salary of her colleague for the first 8 years were $\$32000,\$33600,\$35280,\$37044,\$38896.2,\$40841.01,\$42883.1,\$45027.2$.

Thus, her colleague stats receiving more salary to compare to her from 6^th year.

Conclusion:

Her colleague stats receiving more salary to compare to her from 6^th year.