Question

A new car is purchased for 17200 dollars. The value of the car depreciates at 14.75% per year. To the nearest year, how long will it be until the value of the car is 1900 dollars?

Answer 1

To the nearest year, it will take approximately 7 years for the value of the car to reach $1900.

Step-by-step explanation:

To find out how long it will take for the value of the car to reach $1900, we can set up an equation.

Let x be the number of years it will take.

Using the formula for exponential decay, we can set up the equation: 17200(1 - 0.1475)^x = 1900.

Simplifying the equation, we get (1 - 0.1475)^x = 1900/17200 = 0.1105.

Taking the natural logarithm of both sides, we get x(ln(1 - 0.1475)) = ln(0.1105)

Dividing both sides by ln(1 - 0.1475), we get x ≈ ln(0.1105)/ln(1 - 0.1475).

Using a calculator, we find that x ≈ 7.2. Rounding to the nearest year, it will take approximately 7 years for the value of the car to reach $1900.

Answer 2

6 years

Step-by-step explanation:

We know

A new car is purchased for 17200 dollars.

The value of the car depreciates at 14.75% per year.

To the nearest year, how long will it be until the value of the car is 1900 dollars?

Let's set up an equation to solve for the number of years, represented by 't':

$17200 - (0.1475 · $17200 · t) = $1900

17200 - (2537t) = 1900

2537t = 15300

t ≈ 6 years

So, the answer will be 6 years.