Question

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Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers throughout the season. Each year, he has increased his fee by the same amount. The table shows what Elliot charged each customer for two given years of his business:

(TABLE ON PINNED SCREENSHOT)

A. What is the rate of change and initial value for Elliot's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Elliot charges each year.

Answer 1

Given the table of charges for each customer in the given years, find the rate of change , initial value of Elliot's business and equation representing the charge each year

Explanation:

1. let the initial value of Elliot's business be 'c' , the yearly increase be 'm' and the number of years be 'x'
2. from the table we have the fees charged in the year $2000$ to be $\ 750$ .
3. Since, the business started in  $2000$ the initial value is , $c=750$    
4. from the table we have fees charged in the year $2010$ to be $\ 1350$.
5. hence we get, $x=10\ yrs,\ c=750,\ m=?$                                                                   [tex]10m=1350-750\\ m=\$60[/tex]          
6. now the rate of change is given as, $r=\frac{m}{c}(100) \%$                                              [tex]->r=\frac{60}{750}(100)\\ ->r=8\%[/tex]           -------->ANSWER  
7. now let the fees Elliot charges each be 'y', then we have 'y' as linear function of 'x' number of years as,                                                                         $y=mx+c$           ->m-slope (yearly increase), c-intercept(initial value)                        $y=60x+750$   ------>ANSWER