SOLUTION: [Exponential functions] A computer valued at $6500 depreciates at the rate of 14.3% per year. I need to write a function that models the value of the computer and find the va

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Question 254425: [Exponential functions]
A computer valued at $6500 depreciates at the rate of 14.3% per year.
I need to write a function that models the value of the computer and find the value of the computer after three years.
At first I wrote y=6500(1.143)^x as the function, but when I checked in the back of the textbook, it said y=6500(0.857)^x. How did they get that number?
Thank you!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
it depreciates at the rate of 14.3% per year.

this means that the value drops by 14.3% per year.

14.3% / 100% = .143

your equation increased the value by 14.3% per year.

you added .1453*6500 to 6500 to get:

.

when you factor out the 6500, you get:

= .

that does it for one year.

for n years, you then raised to the exponent of n to get:

.

your equation should have the decreased the value by 14.3% per year.

you needed to subtract .143*6500 from 6500 to get:

.

when you factor out the 6500, you get:

=

that does it for one year.

for n years, you then raised to the exponent of n to get:

where you used x, I used n.

if you prefer to use x, just replace n with x.

graph of looks like this.

the y values of the graph are in hundreds.

6000 = 60
7000 = 70
6500 = 65, etc.

the only x values you are interested are when x is positive.

those values are to the right of the y-axis which is the vertical line when x = 0.

you can see that as x increases, the value of y increases.

graph of looks like this.

you can see that as x increases, the value of y decreases.