Final answer:
The initial value of the car is $26,000 and the value after 12 years is approximately $8,399.03.
Step-by-step explanation:
The exponential function given for the dollar value of a car model is vt=26,000(0.86)ᵀ. To find the initial value of the car, we need to substitute t = 0 into the function. This gives us v0 = 26,000(0.86)⁰ = 26,000. Therefore, the initial value of the car is $26,000.
To find the value of the car after 12 years, we substitute t = 12 into the function. This gives us v12 = 26,000(0.86)¹² ≈ 8,399.03. Therefore, the value of the car after 12 years is approximately $8,399.03.