Question

A manufacturing plant earned

$
80
$80dollar sign, 80 per man-hour of labor when it opened. Each year, the plant earns an additional
5
%
5%5, percent per man-hour.
Write a function that gives the amount
A
(
t
)
A(t)A, left parenthesis, t, right parenthesis that the plant earns per man-hour
t
tt years after it opens.

Answer 1

Answer : A(t)=80⋅1.05*t

Based on khan academy

Answer 2

Explanation:

Each year, the plant earns an additional 5 percent per man-hour. This means that the increase in earnings is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the amount earned after t years.

t represents the number of years.

P represents the initial amount earned.

r represents rate of growth.

From the information given,

P = $800

r = 5% = 5/100 = 0.05

Therefore, the function that gives the amount after t years is

A = 800(1 + 0.05)^t

A = 800(1.05)^t