SOLUTION: A certain type of notebook earned a stationary company $12,000 in profit the first year and $22,000 the third year. Assume the relationship between years on the market and profit

Algebra ->  Linear-equations -> SOLUTION: A certain type of notebook earned a stationary company $12,000 in profit the first year and $22,000 the third year. Assume the relationship between years on the market and profit       Log On


   

Question 204000: A certain type of notebook earned a stationary company $12,000 in profit the first year and $22,000 the third year. Assume the relationship between years on the market and profit is linear. Use ordered pairs of t, years on the market, and p, profit to write an equation of the relationship. Use the equation to predict the profit the fifth year.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Let Profit,p = x . *note: values = 1x10%5E3

Also, let years,t = y

Given: system%28x%5B1%5D=12%2Cx%5B2%5D=22%2Cy%5B1%5D=1%2Cy%5B2%5D=3%29}
Via Point Slope Form,
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%283-1%29%2F%2822-12%29=2%2F10=1%2F5

Via Slope-Intercept Form, y=mx%2Bb
Thru point (x%5B1%5D,y%5B1%5D)=(12,1)
1=%281%2F5%29%2812%29%2Bb
b=1-12%2F5=%285-12%29%2F5=-7%2F5
Also, thru point (22,3)
3=%281%2F5%29%2822%29%2Bb
b=3-22%2F5=%2815-22%29%2F5=-7%2F5

Then, it follows ---> y=%281%2F5%29x-7%2F5

When, t=y= 5 years,
5=%281%2F5%29x-7%2F5
5%2B7%2F5=%281%2F5%29x ---> %2825%2B7%29%2F5=%281%2F5%29x
32%2Fcross%285%29=%281%2Fcross%285%29%29x
highlight%28red%28x=32x10%5E3%29%29, (Answer)



Thank you,
Jojo