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Question 956423: I am doing this project in math about car depreciation. Our teacher wants us to find the exponential function best fit for each car in the form y=Ce^rx. The three cars I picked was a ford escape, chevy impala, and toyota camry.
For the ford the exponential fit is y=2164e^-0.183x
The Chevy exponential fit is y=23347e^-0.188x
The Toyota exponential fit is y=20536e^-0.102x
I guess my question is how do I find the depreciation for each car?
And my other question my teacher wants to know what does C represent, and what does r represent? The teacher said that in the equation y=Ce^rx, y represents suggested retail and x is the age of car in years
For C I said it represents suggested retail as well, and r represents annual depreciation. Thanks for any and all help
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am doing this project in math about car depreciation. Our teacher wants us to find the exponential function best fit for each car in the form y=Ce^rx. The three cars I picked was a ford escape, chevy impala, and toyota camry.
For the ford the exponential fit is y=2164e^-0.183x
The Chevy exponential fit is y=23347e^-0.188x
The Toyota exponential fit is y=20536e^-0.102x
I guess my question is how do I find the depreciation for each car?
And my other question my teacher wants to know what does C represent, and what does r represent? The teacher said that in the equation y=Ce^rx, y represents suggested retail and x is the age of car in years
For C I said it represents suggested retail as well, and r represents annual depreciation.
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Thanks Stanbon for looking at my problem. So for this car project our teacher wanted us to do a scatter plot on excel and that is where I found the exponential best fit for all three cars, maybe I put the information in wrong.
For the ford escape brand new is $22764,
1yr old with 12000 miles is 15268,
2 yr old 24000mi is 14741,
3yrs old and 36000mi is 12505,
4yrs old and 48000 is 10351, and
5 yrs old is 8440,
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C should be the original value of the car:: i,e. 22764
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retail price = (original price)*(e^rx)
Note;: I can't tell from your post whether (?) is e^(rx) or (e^r)*x
I'm going to assume it is e^(rx)
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When x = 1, e^(r*1) = 15268/22764 = 0.6707
Then r = ln(0.6707) = -0.3994
So you have 15268 = 22764*e^(-0.3994x)
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When x = 2, e^(2r) = 14741/22764 = 0.6476
Then 2r = ln(0.6476) = -0.4345
r = -0.2173
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etc.
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Look this over. See if it helps.
Cheers,
Stan H.
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