A car was bought in
February 1, 2015 for
$ 25 , 000 , and its value depreciates by
1.5 % every single month. The value of the car
m months since
February 1, 2015 is given by the formula
V ( m )

To find the value of the car on June 1, 2017, we'll break down the problem into steps:

1. Find the number of months between February 1, 2015, and June 1, 2017:

   • From February 1, 2015, to February 1, 2017, there are exactly 24 months.
   • From February 1, 2017, to June 1, 2017, there are 4 more months.

   Therefore, the total number of months, $m$, is: $m = 24 + 4 = 28 \text{ months}$

2. Determine the decay factor $d$: The car depreciates by 1.5% every month, which means it retains 98.5% of its value each month. So the decay factor $d$ is: $d = 1 - 0.015 = 0.985$

3. Use the given formula to find the car's value after $m = 28$ months:

   The formula for the value of the car after $m$ months is: $V(m) = 25,000 \times (d)^m$ Substituting the values for $d$ and $m$: $V(28) = 25,000 \times (0.985)^{28}$

Now, let's calculate the value.

The value of the car on June 1, 2017, after 28 months of depreciation, is approximately $16,373.99, rounded to the nearest cent.

Would you like further details or explanations? Here are some related questions for deeper understanding:

1. What would be the car's value after 3 years of depreciation?
2. How does the car's value change if the depreciation rate is increased to 2% per month?
3. How many months would it take for the car's value to drop below $10,000?
4. How can we model depreciation with more complex factors, such as varying monthly rates?
5. What is the difference between exponential and linear depreciation?

Tip: In problems with percentage decay or growth, using the decay or growth factor simplifies calculations significantly.