A function that gives the amount that the plant earns per man-hour t years after it opens is ![\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}](https://tex.z-dn.net/?f=%5Cmathrm%7BA%7D%28%5Cmathrm%7Bt%7D%29%3D80%20%5Ctimes%201.05%5E%7B%5Cmathrm%7Bt%7D%7D)
<h3><u>Solution:</u></h3>
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:
![=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052](https://tex.z-dn.net/?f=%3D%2880%20%5Ctimes%201.05%29%2B5%20%5C%25%20%5Ctext%20%7B%20of%20%7D%2880%20%5Ctimes%201.05%29%3D%2880%20%5Ctimes%201.05%29%281.05%29%3D80%20%5Ctimes%201.052)
Similarly Amount earned by plant after three years ![=80 \times 1.05^{t}](https://tex.z-dn.net/?f=%3D80%20%5Ctimes%201.05%5E%7Bt%7D)
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%20%5Ctext%20%7B%20Amount%20earned%20by%20plant%20after%20%7D%20t%20%5Ctext%20%7B%20years%20%7D%3D80%20%5Ctimes%201.05%5E%7Bt%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Ctext%20%7B%20Required%20function%20%7D%20%5Cmathrm%7BA%7D%28t%29%3D80%20%5Ctimes%201.05%5E%7Bt%7D%7D%5Cend%7Barray%7D)
Hence a function that gives the amount that the plant earns per man-hour t years after it opens is ![\mathrm{A}(t)=80 \times 1.05^{t}](https://tex.z-dn.net/?f=%5Cmathrm%7BA%7D%28t%29%3D80%20%5Ctimes%201.05%5E%7Bt%7D)
.09 times 6 is .54, I hope this helps
Answer: 15+X=27
Step-by-step explanation: 15+X=27 X Represents How Much More Is Added
Your answer is (x-8) (x-6)