Question

Lorrie bought a new car for $22,234 and a friend who sells used cars told her that she could expect the car to depreciate by about 10% a year for the next 5 years. how long will it take for the car to have a value of $10,000? round to the nearest tenth of a year.

Answer 1

To find the number of years it will take for the car to depreciate to $10,000, set up an equation and solve for the number of years using logarithms.

Step-by-step explanation:

To solve this problem, we need to find the number of years it will take for the car to depreciate to $10,000. The car is depreciating by 10% each year, so the value after each year can be found by multiplying the previous year's value by 0.9.

We can set up an equation to represent this:

$22,234 * (0.9)^(number of years) = $10,000

Now, we can solve for the number of years by taking the logarithm of both sides:

log($22,234) + number of years * log(0.9) = log($10,000)

Using a calculator, we find that the number of years is approximately 4.2. So, it will take about 4.2 years for the car to have a value of $10,000.