Respuesta :
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]
