Answer: it will take 8 years.
Explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^ t
Where
A represents the value of the after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
P = 24900 dollars
A = 14200 dollars
r = 6.5% = 6.5/100 = 0.065
Therefore
14200 = 24900(1 - 0.065)^t
14200/24900 = (0.935)^t
0.5701 = (0.935)^t
Taking log of both sides to base 10
Log 0.5701 = log0.935^t = tlog0.935
- 0.22 = t × - 0.0292
t = - 0.22/- 0.0292
t = 8 years