MATH SOLVE

3 months ago

Q:
# Dwight has a new job that guarantees a six percent raise for each year with the company. His initial salary is $52,000 per year. Which equation models Dwight's salary after t years?A) y = 52,0000.06t B) y = 52,0001.06t C) y = 52,000(0.06)t D) y = 52,000(1.06)t

Accepted Solution

A:

Dwight's salary after t year is represented by [tex]\mathrm{y}=52000\left(1.06^{t}\right)[/tex]Solution:Given that Dwight has a new job that guarantees a six percent raise for each year with the company.
His initial salary is $52,000 per year.
Need to determine equation which models Dwight's salary after t years
Dwight's initial salary = $52,000 per year.
As job guarantees a six percent raise for each year
Dwight's salary after 1 year = 52000 + 6% of 52000 = 52000 + 0.06 x 52000 = 52000 (1.06)Dwight's salary after 2 year = (52000 x 1.06) + 6 % of (52000 x 1.06) [tex]\begin{array}{l}{=(52000 \times 1.06)+0.06 \times(52000 \times 1.06)} \\\\ {=(52000 \times 1.06)(1.06)=52000 \times 1.06^{2}}\end{array}[/tex][tex]\begin{array}{l}{\text { Similarly Dwight's salary after } 3 \text { year }=52000 \times 1.06^{3}} \\\\ {\Rightarrow \text { Dwight's salary after } t \text { year }=52000 \times 1.06^{t}}\end{array}[/tex]Hence Dwight's salary after t year is represented by = [tex]52000\left(1.06^{t}\right)[/tex]