Answer: [tex]y = 1,500(0.7)^x\ \text{and }y = 1,500 - 300x[/tex]
Step-by-step explanation:
Given : Ron buys a lawnmower for $1,500. The salesperson says the value will depreciate about 30% per year (r=0.3) over the next few years.
The exponential decay equation is given by :-
[tex]y=A(1-r)^x[/tex], where A is the initial amount , r is rate of decay and x is the time period.
Then , the equation of depreciation for Ron :-
[tex]y=1500(1-0.3)^x=1500(0.7)^x[/tex]
However, his neighbor says it is likely to depreciate about $300 per year, which is linear depreciation.
The linear equation is given by :-
[tex]y=ax+c[/tex], where 'c' is the initial amount and 'a' is the rate of change.
Then equation of depreciation for his neighbor :-
[tex]y=-300x+1500=1500-300x[/tex]
Thus , the system could be used to determine when the two depreciation models will give the same value for the lawnmower:-
[tex]y = 1,500(0.7)^x\ \text{and }y = 1,500 - 300x[/tex]
