Final answer:
The model to describe the yearly 8% depreciation in the value of a car bought for $20,000 is f(t) = 20,000(0.92^t), where t represents the number of years. So the correct answer is option A.
Step-by-step explanation:
This model represents depreciation of 8% per year, which means that the value of the car reduces by 8% each year. Multiplying the initial value of $20,000 by 1.08 represents a decrease of 8%.To represent the depreciation of a car's price by 8% yearly, we need to use an exponential decay model.
The correct expression for the value of the car after t years is given by the function f(t) = 20,000(0.92t), where 0.92 is the decay factor obtained by subtracting the 8% depreciation (0.08) from 1. Over time, this model shows how the price of the car decreases at an 8% rate annually.
The initial price of the car is $20,000, and applying the formula for each year, the value of the car will be $20,000 multiplied by 0.92 raised to the power of the number of years t. Each year, the car's value will be 92% of its previous year's value, reflecting a continuous decrease of 8% per year.