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A new car worth ​$24 comma 000 is depreciating in value by ​$4 comma 000 per year. After how many years will the​ car's value be ​$4 comma 000​?

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Part 1
After
  
enter your response here ​years, the​ car's value will be ​$4 comma 000.

1 answer

To find out how many years it takes for the car's value to depreciate from $24,000 to $4,000 at a rate of $4,000 per year, we can set up the following equation:

  1. The initial value of the car is \( V_0 = 24,000 \).
  2. The depreciation per year is \( d = 4,000 \).
  3. We want to find the time \( t \) in years when the value \( V \) is $4,000.

The formula for the value of the car after \( t \) years is:

\[ V = V_0 - (d \times t) \]

Setting \( V = 4,000 \), we get:

\[ 4,000 = 24,000 - (4,000 \times t) \]

Next, rearranging this equation:

\[ 4,000 \times t = 24,000 - 4,000 \] \[ 4,000 \times t = 20,000 \] \[ t = \frac{20,000}{4,000} \] \[ t = 5 \]

Thus, after 5 years, the car's value will be $4,000.