Your car costs $42,500 when you purchased it in 2015l the value of the car decreases by 14% annually. How much will your car be worth in 7 years? Round your answer to the nearest dollar

To determine the value of your car after 7 years, given that it decreases by 14% annually, we can use the formula for exponential decay:

\[ V = P \times (1 - r)^t \]

where:
- $ V $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car,
- $ r $ is the annual depreciation rate,
- $ t $ is the number of years.

Given:
- $ P = 42500 $ dollars,
- $ r = 0.14 $,
- $ t = 7 $ years.

Plugging in the values, we get:

\[ V = 42500 \times (1 - 0.14)^7 \]
\[ V = 42500 \times 0.86^7 \]

First, calculate $ 0.86^7 $:

\[ 0.86^7 \approx 0.3975 \]

Now multiply this result by the initial value:

\[ V = 42500 \times 0.3975 \]
\[ V \approx 16893.75 \]

Rounding to the nearest dollar:

\[ V \approx 16894 \]

So, the car will be worth approximately $16,894 after 7 years.

Do you want details or have any questions?

Here are 5 related questions for further exploration:
1. What would the value of the car be after 10 years with the same depreciation rate?
2. How much value does the car lose in the first year?
3. What is the total percentage decrease in value after 7 years?
4. How does the value change if the annual depreciation rate is 10% instead of 14%?
5. If the car's value decreases exponentially, what is its half-life in terms of value?

**Tip:** Understanding exponential decay is crucial in many fields, including finance, physics, and environmental science. It describes processes that decrease at a rate proportional to their current value.

Your car costs $42,500 when you purchased it in 2015. The value of the car decreases by 14% annually. How much will your car be worth in 7 years? Round your answer to the nearest dollar.

Learn how to calculate the depreciation of a car purchased for $42,500 with a 14% annual decrease in value. Using the exponential decay formula, discover how much the car will be worth after 7 years. Suitable for high school students in Grades 9-12.

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