Answer: a) To model the value of the car after "x" months, we can use the formula for exponential decay:
value after x months = initial value * (decay rate)^x
where the initial value is $4500 and the decay rate is 0.95 (100% - 5% = 95%):
value after x months = 4500 * 0.95^x
b) To find the value of the car after 8 months, we can substitute x = 8 into the equation above:
value after 8 months = 4500 * 0.95^8
value after 8 months = 4500 * 0.6634
value after 8 months = $2985.30
Therefore, the car will be worth approximately $2,985.30 after 8 months.
c) To find when the car's value will be $2,000, we can set the equation above equal to 2000 and solve for x:
2000 = 4500 * 0.95^x
0.95^x = 2000/4500
0.95^x = 0.4444
Taking the logarithm of both sides with base 0.95:
x = log(0.4444)/log(0.95)
x ≈ 14.8
Therefore, the car's value will be $2,000 after approximately 15 months (rounded to the nearest whole month).
Explanation: