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 ttt years after it opens.

Answer 1

Answer:

$A(t)=80(1.05)^t$

Step-by-step explanation:

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

The plant earns an additional 5% for every additional man-hour t.

This can be modeled using the function:

$A(t)=P(1+r)^t$

where Initial Amount Earned, P=80

Rate of Increase, r=5%=0.05

Therefore, the function that models the amount earned at any time t is:

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