Question

A new car costs $30,000; it loses 10% of its value each year. Maintenance is $500 the first year and increases by 20% annually. Find a formula for In, the value lost by the car in year n.

Answer 1

The formula for the value lost by the car in year n is In = P - P(1 - r)^n, where In is the value lost, P is the initial value of the car, r is the decay rate (0.1), and n is the number of years.

Step-by-step explanation:

To find a formula for the value lost by the car in year n, we can use the concept of exponential decay. The formula for exponential decay is V = P(1 - r)^n, where V is the value after n years, P is the initial value, r is the decay rate, and n is the number of years.

Given that the car loses 10% of its value each year, the decay rate r would be 0.1. The initial value P is $30,000.

So, the formula for the value lost by the car in year n is: In = P - P(1 - r)^n.