Question

A new car is purchased for $49,000 and over time its value depreciates by one half every 5 years. What is the value of the car 21 years after it was purchased, to the nearest hundred dollars?

Answer 1

To find the value of the car 21 years after it was purchased, we can use the concept of exponential decay. The value of the car can be calculated using the formula V(t) = 49000 * (1/2)^(t/5), where t is the number of years. Substituting t = 21 into the equation, we find that the value of the car 21 years after it was purchased is approximately $2,421.37.

Step-by-step explanation:

To find the value of the car 21 years after it was purchased, we can use the concept of exponential decay. Since the value of the car depreciates by one half every 5 years, we can express the value of the car after t years as:

V(t) = 49000 * (1/2)^(t/5)

Substituting t = 21 into the equation, we get:

V(21) = 49000 * (1/2)^(21/5)

Calculating this value, we find that the value of the car 21 years after it was purchased is approximately $2,421.3