Car Depreciation and Exponential Functions

The video tutorial explains how to calculate the depreciation of a car using an exponential function. It starts by introducing the concept of car depreciation, which is typically 15% per year. The tutorial then models the car's value using an exponential function, where the base represents the percentage of value retained each year. The function is simplified, and the car's value after eight years is calculated to be approximately $5,177. The video concludes by explaining the significance of the base in the function, which indicates the percentage of value retained annually.

What is the average annual depreciation rate for a car?

• 25%

• 20%

• 10%

• 15%

In the exponential function F(x) = A(B)^x, what does 'A' represent?

• The depreciation rate

• The base of the function

• The number of years

• The initial value of the car

How is the base 'B' in the exponential function calculated?

• R + 1

• 1 - R

• 1 + R

• R - 1

What is the value of 'R' when the depreciation rate is 15%?

• -1.15

• 1.15

• -0.15

• 0.15

What is the simplified form of the function V(T) = 19,000 x (1 + -0.15)^T?

• V(T) = 19,000 x 0.85^T

• V(T) = 19,000 x 1.85^T

• V(T) = 19,000 x 1.15^T

• V(T) = 19,000 x 0.15^T

After eight years, what is the approximate value of the car?

• $7,200

• $6,000

• $5,177

• $4,500

What is the purpose of rounding the car's value to the nearest dollar?

• To make the value easier to understand

• To simplify calculations

• To increase accuracy

• To comply with financial regulations

Why is the base of the exponential function 0.85?

• Because the car retains 85% of its value each year

• Because the car retains 15% of its value each year

• Because the car loses 15% of its value each year

• Because the car loses 85% of its value each year

What does the base of the exponential function represent?

• The percentage of value lost each year

• The number of years

• The percentage of value retained each year

• The initial value of the car

If a car retains 85% of its value each year, what percentage does it lose?

• 10%

• 25%

• 15%

• 20%