Question

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).

Answer 1

Answer:

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

Explanation:

Obtaining the formula

We wish to find a formula that

• Starts at 2816. $f(0 \ years) \ = \ \ \ 2816$
• Reach 0 at 8 years. $f( 8 \ years) \ = \ \ \ 0$
• Depreciates at a constant rate. m

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) :

$f(t) \ = \ m\ t \ + \ b$,

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:

$f ( 0 \ years ) = m \ (0 \ years) + b = \ \ 2816$

$b = \ \ 2816$

So, b = $ 2816.

Now, for the second condition:

$f ( 8 \ years ) = m \ (8 \ years) + \ \ 2816 = \ \ 0$

$m \ (8 \ years) = \ - \ \ 2816$

$m = \frac{\ - \ \ 2816}{8 \ years}$

$m = \frac{\ - \ \ 2816}{8 \ years}$

$m = \ - \ 352 \frac{\ }{years}$

So, our formula, finally, its:

$f(t) \ = \ - \ 352 \ \frac{\ }{years} \ t \ + \ \ \ 2816$

After 5 years

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

$f(5 \ years) \ = \ - \ 352 \ \frac{\ }{years} \ 5 \ years \ + \ \ \ 2816$

$f(5 \ years) \ = \ - \ \ 1760 + \ \ \ 2816$

$f(5 \ years) \ = \ 1056$