Question

Ron buys a lawnmower for $1,500. The salesperson says the value will depreciate about 30% per year over the next few years. However, his neighbor says it is likely to depreciate about $300 per year.

Which system could be used to determine when the two depreciation models will give the same value for the lawnmower?

Answer 1

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Answer 2

well the 2 models are linear and exponential:
Linear model
\[V = 1500 -300t\]
exponential model
\[V = 1500(1-0.3)^t = 1500(0.7)^t\]
To find when they give same value, set 2 equations equal and solve for t
\[1500(0.7)^t = 1500 - 300t\]
Unfortunately you will have to estimate since there is no way to solve this algebraically
If this is a calculus course, i would use newtons method for approximating zeros

Otherwise graph both functions and estimate where they intersect

Answer 3

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