Car Value Depreciation and Exponential Decay

The video tutorial explains how to model a word problem involving exponential decay. It uses the example of a car purchased in 2008 for $17,000, which decreases in value by 27% each year. The tutorial guides viewers through deriving an exponential function to represent the car's value over time, using the formula y = 17000 * 0.73^t, where t is the number of years since 2008. The video emphasizes understanding the role of exponents in modeling exponential growth or decay.

What type of mathematical problem is being discussed in the video?

• Exponential growth or decay

• Linear growth

• Logarithmic function

• Quadratic equation

In what year was the car purchased according to the problem statement?

• 2010

• 2012

• 2005

• 2008

What is the initial value of the car when it was purchased?

• $20,000

• $18,500

• $17,000

• $15,000

By what percentage does the car's value decrease each year?

• 5%

• 10%

• 27%

• 15%

How do you calculate the car's value after the first year?

• Subtract 27% from the initial value

• Multiply by 0.73

• Multiply by 0.27

• Add 27% to the initial value

What is the value of the car after two years if it decreases by 27% each year?

• $9,000

• $12,000

• $17,000

• Multiply the first year's value by 0.73 again

What mathematical concept helps in calculating the car's value over multiple years?

• Division

• Exponents

• Subtraction

• Addition

What does the exponent in the formula represent?

• The initial value of the car

• The number of years

• The percentage decrease

• The final value of the car

What is the general formula for the car's value over time?

• y = 17000 + 0.73t

• y = 17000 * t

• y = 17000 * 0.73^t

• y = 17000 - 0.27t

How can you use the formula to find the car's value after 7 years?

• Multiply 17000 by 7

• Plug in 7 for t in the formula

• Subtract 7 from 17000

• Add 7 to 17000