Calculating Car Depreciation Using Exponential Function

TLDR; The video discusses using an exponential function to model car depreciation and calculates the approximate value of a car after eight years.

The average car depreciation rate is 15% per year.

This means that the value of a car decreases by 15% of its current value each year.

If you purchase a car for $19,000, the goal is to determine its approximate value after eight years.

We can model the value of a car using an exponential function in the form F(X) = A(B) raised to the power of X.

The exponential function F(X) = A(B) raised to the power of X is broken down into its components.

The base (B) is equal to 1 + the depreciation rate expressed as a decimal, where the depreciation rate (R) is -15% in this case.

The initial amount (A) represents the initial price of the car, and X represents the age of the car in years.

The exponential function V(T) = 19,000 x 0.85 raised to the power of T is derived to determine the approximate value of the car after eight years.

Here, V(T) represents the value of the car in dollars, and T is the age of the car in years.

Using the calculated function, the approximate value of the car after eight years is determined to be $5,177.

This is obtained by evaluating V(8) = 19,000 x 0.85 raised to the power of 8.

The base of the exponential function, which is 0.85, represents the percentage of value the car retains each year.

In this case, as the car loses 15% per year, it retains 85% of its value each year, hence the base being 0.85.

The speaker concludes by pointing out the significance of the base 0.85 in the exponential function and its relationship to the car's retained value.

The explanation of the base value provides clarity on the modeling of car depreciation using the exponential function.