Answer: after 6 years.
Step-by-step 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 car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate at which the value is decreasing.
From the information given,
P = 3000
A = < 10000
r = 16% = 16/100 = 0.16
Therefore
10000 = 30000(1 - 0.16)^ t
1000/30000 = (0.84)^t
0.333 = (0.84)^t
Taking log of both sides to base 10
Log 0.333 = log0.84^t = tlog0.84
- 0.4772 = t × - 0.0757
t = - 0.4772/ - 0.0757 = 6.3 years
