Answer:
Step-by-step explanation:
We apply the exponential decay formula, which is represented as
A = P(1 - r)^t
Where
A signifies the car's value after t years.
t denotes the number of years.
P is the initial car value.
r signifies the decay rate.
Based on the provided information,
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 logarithms on both sides leads to
Log 7.519 = 7 log(1 - r)
0.876 = 7 log(1 - r)
Log (1 - r) translates to 0.876/7 = 0.125
By applying inverse logarithm, it results in
10^log1 - r equals 10^0.125
1 - r = 1.33
Thus, r = 1.33 - 1 = 0.33
We now have the expression
A = 20300(1 - 0.33)^t
A = 20300(0.67)^t
Thus, in 2007,
t = 2007 - 1997 = 10 years
The projected value equals
A = 20300(0.67)^10
A = $370
