Final answer:
To determine when the car will be worth $15,000, we can use the concept of exponential decay. The car will be worth $15,000 after about 6.82 years.
Step-by-step explanation:
To determine when the car will be worth $15,000, we can use the concept of exponential decay. The formula to calculate the value of an object after a certain number of years with a constant decay rate is: V = P * (1 - r)^n, where V is the final value, P is the initial value, r is the decay rate, and n is the number of years.
In this case, the initial value is $23,000, the decay rate is 7% or 0.07 (converted to decimal), and the final value is $15,000.
Substituting these values into the formula, we have: 15000 = 23000 * (1 - 0.07)^n. To solve for n, we need to isolate the exponent: (1 - 0.07)^n = 15000/23000.
Using logarithms, we can solve for n: n = log(15000/23000) / log(1 - 0.07). Evaluating this expression, we find that n is approximately 6.82 years. Therefore, the car will be worth $15,000 after about 6.82 years.