SOLUTION: Express the annual rate of depreciation r as a function of t if a new car was purchased for 18,300 and sold t years later for 7,500

Question 1076469: Express the annual rate of depreciation r as a function of t if a new car was purchased for 18,300 and sold t years later for 7,500
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula would be:

f = p - r*t

p is 18,300
f is 7,500
t is number of years
r is the average rate of depreciation for each year.

formula becomes:

7,500 = 18,300 - r*t

you would solve this equation for r as follows:

start with 7,500 = 18,300 - r*t

add r*t to both sides of the equation and subtract 7,500 from both sides of the equation to get:

r*t = 18,300 - 7,500

divide both sides of the equation by t to get:

r = (18,300 - 7,500) / t

for example:

if t = 5 years, then the formula becomes:

r = (18,300 - 7,500) / 5

solve for r to get r = 2,160 per year.

the car depreciates by an average of 2,160 each year.

the price of the new car is 18,300
after 1 year, the value is 18,300 - 2,160 = 16,140
after 2 years, the value is 16,140 - 2,160 = 13,980
after 3 years, the value is 13,980 - 2,160 = 11,820
after 4 years, the value is 11,820 - 2,160 = 9,660
after 5 years, the value is 9,660 - 2,160 = 7,500

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