A computer is purchased for $2816 and depreciates at a constant rate to $0 in 8 years. Find a formula for the value, V , of the computer after t years have passed. Then use this formula to give the value of the computer after 5 years. (This is known as "straight-line depreciation" and is a depreciation model often used on tax forms).

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fenixbm fenixbm · Answer 1 · 2019-09-12T05:40:35+02:00

Answer:

The formula its [tex]f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816 [/tex]
After 5 years, the computer value its $ 1056

Explanation:

We wish to find a formula that

We can cover all this requisites with a straight-line equation. (an straigh-line its the only curve that has a constant rate of change) :

[tex]f(t) \ = \ m\ t \ + \ b[/tex],

where m its the slope of the line and b give the place where the line intercepts the y axis.

So, we can use this formula with the data from our problem. For the first condition:

[tex]f ( 0 \ years ) = m \ (0 \ years) + b = \$ \ 2816[/tex]

[tex] b = \$ \ 2816[/tex]

So, b = $ 2816.

Now, for the second condition:

[tex]f ( 8 \ years ) = m \ (8 \ years) + \$ \ 2816 = \$ \ 0[/tex]

[tex] m \ (8 \ years) = \ - \$ \ 2816[/tex]

[tex] m = \frac{\ - \$ \ 2816}{8 \ years}[/tex]

[tex] m = \ - \ 352 \frac{\$ }{years}[/tex]

So, our formula, finally, its:

[tex]f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816 [/tex]

Now, we just use t = 5 years in our formula

[tex]f(5 \ years) \ = \ - \ 352 \ \frac{\$ }{years} \ 5 \ years \ + \ \$ \ 2816 [/tex]

[tex]f(5 \ years) \ = \ - \$ \ 1760 + \ \$ \ 2816 [/tex]

[tex]f(5 \ years) \ = $ \ 1056 [/tex]