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Question

The value of a car after t years is a depreciation can be found by the formula V=m(1-r)^t. If the intitial value, m=$32.620, and the depreciation , r=17%, how long will it take for the value of the car to be less than $9240.

Answer 1

you have all the information you need, you just need to organize it. so:

V = m (1 - r) ^ t

V = 9240
m = 32620
r = 0.17
and t is what you're looking for. so, plugging it all in, you have:

9240 = 32620 (1 - 0.17) ^ t

divide both sides by 32.62 to get:

0.28326 = (1 - 0.17)^t

0.28326 = .83^t

then take the log of both sides to get:

log (0.28326) = t log (0.83)

solve for t and you get:

t = 6.77 years

Answer 2

V=m(1-r)^t

m = 32620
r =0.17
V = 9240

9240 = 32620 (1 - 0.17)^t = 32620 (0.83)^t

0.83^t = 0.28309

Taking the Ln of the 2 sides, we get

t Ln (0.83) = Ln (0.28309) =

t = Ln (0.28309) / Ln (0.83) = 6.77 years


t = approximately 7 years

Answer 3

V=m(1-r)^t.
9240 = 32620(1-.17)^t
924/3262 = .83^t
ln (924/3262) = tln(.83)
t = ln(924/3262)/ln(.83)
t = 6.7696 years
So t = 6.77 years