Understanding Exponential Decay in Car Value

The video tutorial explains how to use the equation v = 37,500 * 0.84^t to determine the value of a car over time. It covers the concept of exponential decay, showing that the car's value decreases by 16% per year. The initial purchase price is identified as $37,500. The tutorial also demonstrates how to calculate the car's value after three years, resulting in approximately $22,226.

What does the equation v = 37,500 * 0.84^t represent?

• The fuel efficiency of a car over time.

• The speed of a car over time.

• The value of a car in dollars over time.

• The maintenance cost of a car over time.

What type of growth or decay does the equation v = 37,500 * 0.84^t represent?

• Exponential decay

• Exponential growth

• Linear decay

• Linear growth

If the base of an exponential equation is between 0 and 1, what does it indicate?

• Exponential growth

• Linear growth

• Exponential decay

• Linear decay

How do you calculate the rate of decrease in an exponential decay equation?

• By adding the base to 1

• By subtracting the base from 1

• By multiplying the base by 100

• By dividing the base by 100

What is the rate of decrease per year for the car's value?

• 20%

• 16%

• 10%

• 25%

What does the 'a' represent in the exponential equation y = a * b^x?

• The time in years

• The rate of decrease

• The initial or starting value

• The base of the equation

What was the initial purchase price of the car?

• $40,000

• $37,500

• $35,000

• $30,000

How do you find the value of the car after a certain number of years?

• By adding the number of years to the initial value

• By substituting the number of years into the equation

• By dividing the initial value by the number of years

• By multiplying the initial value by the rate of decrease

What is the value of the car after three years, rounded to the nearest dollar?

• $30,000

• $25,000

• $22,226

• $20,000

Why do we round down the value of the car after three years?

• Because the tenths place is less than 5

• Because the tenths place is more than 5

• Because the tenths place is exactly 5

• Because the tenths place is irrelevant