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

Answer:

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.

Step-by-step 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;

$y(t) =A(t)$

$a=80$

$r= 6\% =\frac{6}{100}=0.06$

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.