Question

State whether the decay is linear or​ exponential, and answer the associated question. The value of a car is decreasing by 15​% per year. If the car is worth ​$11000 ​today, what will it be worth in two​ years?

Answer 1

The decay of a car's value at 15% per year is exponential. Using the exponential decay formula, the car valued at $11000 today will be worth $7947.50 after two years.

Step-by-step explanation:

The decay in the value of a car is described as decreasing by 15​% per year. This type of decrease is exponential decay, not linear. With an initial value of $11000, we can calculate its future value after two years using the formula for exponential decay: Future value = Present value × (1 - Rate of decay)^Number of periods.

In this case, the present value is $11000, the rate of decay is 15​% or 0.15, and the number of periods is 2 years. So, the calculation is $11000 × (1 - 0.15)^2.

Let's calculate:

1. $11000 × (1 - 0.15) = $11000 × 0.85 = $9350 after the first year.
2. Then $9350 × (1 - 0.15) = $9350 × 0.85 = $7947.50 after the second year.

Therefore, the car will be worth $7947.50 in two years.