Question 974084: I need to know how to input information into a TI-83 Plus to create a graph for an exponential regression function, question.
The question is:
In 2008, Marianna paid $14000 for a used 2005 van. She has been tracking the selling price of the can as time has passed to decide how long to keep the can before replacing it. The data is:
Age (in years): 3, 4, 5, 6, 7, 8
Selling Price ($): 14500, 11600, 8700, 6800, 4300, 3500
(The price corresponds numerically with the order that the years are listed {i.e. year 3 the price would be 14500.})
I also need help how to figure out the price of the van in 2005 and what the annual depreciation rate is.
Thank you so much if you do help me out. I really need to finish my assignment by monday.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Step 1) Hit the STAT key (third column, right under the DEL key)
Step 2) Hit enter to get into the "edit" menu. You'll see three columns with headers L1, L2, L3, etc. They represent list1, list2, etc.
Step 3)Type the age data into L1. Type the price data into L2. Once you're all done with this step, you'll have this in your calculator
Step 4) Hit the "2nd" key (yellow key, top left corner) then hit the MODE button to quit back to the home screen. The data you typed into L1 & L2 will still be there and it hasn't been erased.
Step 5) Hit the STAT key again. Then scroll one time to the right to get to the "CALC" menu.
Step 6) Scroll down to "0:ExpReg" (as shown below) and hit enter
Step 7) Once "ExpReg" is copied to the home screen, hit enter again to have the calculator run the program. The calculator will do its thing and spit this out
Step 8) Since the calculator states that  and 
this means 
So the exponential regression equation is roughly 
Rounded to 3 decimal places, the exponential regression equation is roughly 
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The van was brand new back in 2005. The price of this brand new van is unknown right now.
Three years later, in 2008, she paid $14000. Notice how in year 3, the price listed is 14500, so this suggests she paid for the van near the end of year 3.
Anyways, to find the price of the van at the very beginning, simply plug in x = 0. x represents the age in years. At x = 0, the car is 0 years old, so it is brand new.
 Replace x with 0
 Compute the expression with a calculator
And this value is exactly equal to the value of 'a' above.
The price of the van (completely brand new) back in 2005 was $36,947.34. Make sure to round to the nearest penny, ie the nearest hundredth.
Of course, since the exponential regression isn't perfect, the value above is also going to be a bit off due to error. However, it's as close as we can get with this given info.
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The annual depreciation rate r is the percentage that the car loses in value each year.
We can only get an approximate estimate of r since the exponential regression isn't 100% exact.
The quantity  will help us determine r
It turns out that  is equal to b. So,
r = -0.2556 = -25.56%
The negative r reflects the fact the car is depreciating in value (instead of appreciating).
Therefore, the car is depreciating roughly by 25.56% each year. To put it into simpler terms, the car is losing roughly a quarter of its value each year.
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Jim
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