Question

A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour. Write a function that gives the amount A(t) that the plant earns per man-hour (t) years after it open.

Answer 1

The answer is 
$A(t)=80(1.05)^t$

This equation is of the form y=a(1+r)ˣ, where a is the initial amount, r is the rate of change expressed as a decimal, and x is the amount of time.  In our problem, a is 80; r is 5%, and 5%=5/100 = 0.05; and x is t.  This gives us

$A(t)=80(1+0.05)^t \\ \\A(t)=80(1.05)^t$

Answer 2

The function that represents the amount is formulated below:

$\begin{aligned} \rm{Amount}&=80(1+5/100)^t \end{aligned}$

Given,

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

We need to determine the function that gives the amount A(t) that the plant earns per man-hour (t) years after it open.

Therefore,

The formulated way to represent the amount after t years is given below:

$\rm{Amount}=P(1+r)^t$

Where,

P = Principal amount

r = Rate

t = Time (in years)

Thus, the function that represents the amount is formulated below:

$\begin{aligned} \rm{Amount}&=80(1+5/100)^t\\&=80(1+0.05)^t\\&=80(1.05)^t \end{aligned}$

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