Answer:
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 of decay.
From the information given,
A = $2700
P = $20300
n = 2004 - 1997 = 7 years
Therefore,
20300 = 2700(1 - r)^7
20300/2700 = (1 - r)^7
7.519 = (1 - r)^7
Taking log of both sides, it becomes
Log 7.519 = 7 log(1 - r)
0.876 = 7 log(1 - r)
Log (1 - r) = 0.876/7 = 0.125
Taking inverse log of both sides, it becomes
10^log1 - r = 10^0.125
1 - r = 1.33
r = 1.33 - 1 = 0.33
The expression would be
A = 20300(1 - 0.33)^t
A = 20300(0.67)^t
Therefore, in 2007,
t = 2007 - 1997 = 10 years
The value would be
A = 20300(0.67)^10
A = $370
