aiden accepted a new job at a company with a contract guaranteeing annual raises. let s represent aidens…

aiden accepted a new job at a company with a contract guaranteeing annual raises. let s represent aidens salary after working for n years at the company. the table below has select values showing the linear relationship between n and s. determine how many years aiden would have to work at the company before his salary would reach $88000.\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nn&2&7&9\n\\hline\ns&79000&101500&110500\n\\hline\n\\end{tabular}

aiden accepted a new job at a company with a contract guaranteeing annual raises. let s represent aidens salary after working for n years at the company. the table below has select values showing the linear relationship between n and s. determine how many years aiden would have to work at the company before his salary would reach $88000.\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nn&2&7&9\n\\hline\ns&79000&101500&110500\n\\hline\n\\end{tabular}

Answer

Explanation:

Step1: Find the slope of the linear - relationship

The slope $m$ of a linear equation $S = mn + b$ can be found using two points $(n_1,S_1)$ and $(n_2,S_2)$. Let $(n_1,S_1)=(2,79000)$ and $(n_2,S_2)=(7,101500)$. The slope formula is $m=\frac{S_2 - S_1}{n_2 - n_1}$. $m=\frac{101500 - 79000}{7 - 2}=\frac{22500}{5}=4500$.

Step2: Find the y - intercept

We use the point - slope form $S - S_1=m(n - n_1)$ with the point $(n_1,S_1)=(2,79000)$ and $m = 4500$. $S-79000 = 4500(n - 2)$. $S-79000=4500n-9000$. $S = 4500n+70000$.

Step3: Solve for $n$ when $S = 88000$

Set $S = 88000$ in the equation $S = 4500n+70000$. $88000=4500n + 70000$. Subtract 70000 from both sides: $88000 - 70000=4500n$, so $18000 = 4500n$. Divide both sides by 4500: $n=\frac{18000}{4500}=4$.

Answer:

4