To solve the given problem, we need to find a formula for the value $V(t)$ of the car, in terms of the number of years $t$ since 2005.

Information given:

• Initial value of the car in 2005: $19,500.
• The car depreciates by $550 each year.
• We are looking for a formula for $V(t)$, where $t$ is the number of years since 2005.

Step-by-step solution:

1. Depreciation rate: The car loses $550 each year, so the depreciation rate is linear.
2. Initial value at $t = 0$: In 2005, the car was worth $19,500, so $V(0) = 19,500$.
3. Value after $t$ years: After $t$ years, the car loses $550t$ dollars in value.

The general formula for the value $V(t)$ of the car after $t$ years is: $V(t) = 19,500 - 550t$

This equation represents the linear depreciation of the car's value over time.

Would you like further explanation on how depreciation works or how to apply this formula for specific values of $t$?

Follow-up questions:

1. How would you calculate the value of the car after 10 years?
2. What will the car's value be after 5 years?
3. How many years will it take for the car's value to decrease to $0?
4. What is the car's value in 2020 (i.e., 15 years after purchase)?
5. How would the formula change if the depreciation rate increased to $600 per year?

Tip:

In linear depreciation problems, the rate of change (the amount lost each year) remains constant, making it straightforward to calculate future values or predict when an asset will lose all its value.