Question

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

Answer 1

Dwight's salary after t year is represented by
`\mathrm{y}=52000\left(1.06^(t)\right)`

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)

`\begin{array}{l}{=(52000 * 1.06)+0.06 *(52000 * 1.06)} \\\\ {=(52000 * 1.06)(1.06)=52000 * 1.06^(2)}\end{array}`

`\begin{array}{l}{\text { Similarly Dwight's salary after } 3 \text { year }=52000 * 1.06^(3)} \\\\ {\Rightarrow \text { Dwight's salary after } t \text { year }=52000 * 1.06^(t)}\end{array}`

Hence Dwight's salary after t year is represented by =
`52000\left(1.06^(t)\right)`