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?

The expression 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;

Where;

⇒ Amount after t years

   ⇒ Initial amount

   ⇒ rate of change in amount

    ⇒ Amount of time

In The given data;

t =

So we can say that;

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.

Hence The expression gives the amount the plant earned per a man-hour of labor 3 years after it opened.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .