To solve this problem, we will use the formula for exponential depreciation:

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

Where:

• $V$ is the value of the car after $t$ years,
• $P$ is the initial price of the car,
• $r$ is the depreciation rate (expressed as a decimal),
• $t$ is the time in years.

Given:

• Initial price $P = 16600$ dollars,
• Depreciation rate $r = 9.75\% = 0.0975$,
• Time $t = 8$ years.

Now, let's substitute the values into the formula:

$V = 16600 \times (1 - 0.0975)^8$

$V = 16600 \times (0.9025)^8$

First, calculate $0.9025^8$:

$0.9025^8 \approx 0.4220$

Now, calculate the value of the car:

$V = 16600 \times 0.4220 \approx 7007.20$

So, the value of the car after 8 years is approximately $7007.20.

Would you like further details on how this formula works or any clarification? Here are a few related questions:

1. How does the formula for exponential depreciation differ from linear depreciation?
2. What would happen to the value of the car if the depreciation rate was lower?
3. How do you calculate the depreciation for multiple items at once?
4. How does the concept of depreciation apply to other assets like houses or machinery?
5. If the car were sold after 8 years, how would you calculate its selling price?

Tip: When dealing with exponential decay or growth, always convert percentage rates to decimals by dividing by 100 before applying them in calculations.