Question

A manufacturing plant earned $80 per a man-hour of labor when it opened. Each year, the plant earns an additional 6% per man-hour. Which expression gives the amount the plant earned per a man-hour of labor 3 years after it opened?

Answer 1

The expression
`A(3) =80(1.06)^3` gives the amount the plant earned per a man-hour of labor 3 years after it opened.

Explanation:

Given:

Amount earned by Manufacturing Plant = $80/per man -hour labor

Percent increase in Amount earned by Manufacturing Plant each year = 6%

We need to find the expression gives the amount the plant earned per a man-hour of labor 3 years after it opened.

Solution:

Now we will use the expression;

`y(t)=a(1+r)^t`

Where;

`y(t)` ⇒ Amount after t years

`a` ⇒ Initial amount

`r` ⇒ rate of change in amount

`t` ⇒ Amount of time

In The given data;

`y(t) =A(t)`

`a=80`

`r= 6\% =(6)/(100)=0.06`

t =
`3\ years`

So we can say that;

`A(t)= 80(1+0.06)^t=80(1.06)^t`

To find the amount the plant earned per a man-hour of labor 3 years after it opened we will substitute the value of t as 3.

`A(3) =80(1.06)^3`

Hence The expression
`A(3) =80(1.06)^3` gives the amount the plant earned per a man-hour of labor 3 years after it opened.