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?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[80\cdot 0.06\cdot 0.06\cdot 0.06\]
A
\[80\cdot 0.06\cdot 0.06\cdot 0.06\]
(Choice B)
\[80+0.06\cdot 0.06\cdot 0.06\]
B
\[80+0.06\cdot 0.06\cdot 0.06\]
(Choice C)
\[80(1+0.06)(1+0.06)(1+0.06)\]
C
\[80(1+0.06)(1+0.06)(1+0.06)\]
(Choice D)
\[80+(1+0.06)(1+0.06)(1+0.06)\]
D
\[80+(1+0.06)(1+0.06)(1+0.06)\]

Answer 1

To find the amount the plant earns per man-hour of labor 3 years after it opened, we need to account for the annual increase of 6% compounded over 3 years.

Starting with an initial earning of \$80 per man-hour, the earnings after each year can be calculated as follows:

- After the first year: \( 80 \times (1 + 0.06) \)
- After the second year: \( 80 \times (1 + 0.06)^2 \)
- After the third year: \( 80 \times (1 + 0.06)^3 \)

This can be expressed as:
\[
80 \times (1.06)^3
\]

The correct expression for the amount the plant earned per man-hour of labor 3 years after it opened is represented as:
\[
80(1 + 0.06)(1 + 0.06)(1 + 0.06)
\]

Thus, the correct choice is:

**(Choice C)** \( 80(1 + 0.06)(1 + 0.06)(1 + 0.06) \)