Question

Leo buys a corvette for $60000. It depreciates 10% of its value each year. In addition to identifying whether this models growth or decay, identify the function that models the value of this car in terms of years (t).

Answer 1

Leo's Corvette's value is modeled by exponential decay, with the decay function being V(t) = $60,000(1 - 0.1)^t, where V(t) is the value of the car after t years.

Step-by-step explanation:

The scenario presented indicates that the value of Leo's Corvette is experiencing exponential decay since it depreciates by 10% each year. To model the car's value over time, we can use an exponential decay function. The initial value of the car is $60,000, and the decay rate is 10% or 0.1 annually. The value V of the car after t years can be represented by the function:

V(t) = P(1 - r)^t

Where:

• V(t) represents the value of the car after t years
• P is the initial value of the car, which is $60,000
• r is the annual depreciation rate, which is 0.1 (or 10%)
• t represents the number of years

Therefore, the function that models the value of the Corvette in terms of years (t) is:

V(t) = $60,000(1 - 0.1)^t