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 opens.

A function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}[/tex]Solution:Given that  A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour. Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  Amount earned by plant when it is opened = $80 per man-hour As it is given that each year, the plants earns an additional of 5% per man hour So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05) Amount earned by plant after two years is given as:[tex]=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052[/tex]Similarly Amount earned by plant after three years [tex]=80 \times 1.05^{t}[/tex][tex]\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}[/tex]Hence a function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(t)=80 \times 1.05^{t}[/tex]