

A $29,559 car depreciates by 20% per year.  What is the starting value, B, that you will use in the exponential model to estimate the value of the car after t years?

Round your answer to the nearest cent.


To model the depreciation of the car using an exponential function, we use the formula:

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

where:
- $ V(t) $ is the value of the car after $ t $ years,
- $ B $ is the initial value of the car,
- $ r $ is the rate of depreciation per year, and
- $ t $ is the number of years.

In this case:
- The car's initial value is $ B = 29,559 $ dollars.
- The depreciation rate $ r = 20\% = 0.20 $.

Therefore, the starting value $ B $ that will be used in the exponential model is:

\[
B = 29,559
\]

So, the starting value $ B $ is $ 29,559.00 $ dollars.

Would you like more details, or have any questions? Here are some related questions:

1. How do you calculate the value of the car after 5 years?
2. What will be the car's value after 3 years?
3. How would the model change if the depreciation rate was 15% instead of 20%?
4. How do you find the rate at which the car loses half of its value?
5. How can we use logarithms to solve for the number of years it takes for the car to depreciate to a certain value?

**Tip:** Always convert percentage rates to decimals when using them in mathematical formulas.

A $29,559 car depreciates by 20% per year. What is the starting value, B, that you will use in the exponential model to estimate the value of the car after t years? Round your answer to the nearest cent.

Learn how to find the starting value of a $29,559 car in an exponential depreciation model, with a 20% annual depreciation rate. This solution uses the exponential decay formula and is ideal for high school students learning about algebra and depreciation.

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