Exploring Exponential Growth and Decay Word Problems

The video tutorial covers exponential functions, focusing on growth and decay. It explains the general formula for exponential functions and provides examples of exponential growth and decay. The tutorial includes a detailed explanation of exponential growth using a population graph and exponential decay using a basketball tournament. Two examples are provided: one on car depreciation as an example of exponential decay and another on savings account growth as an example of exponential growth. The video concludes with calculations of future values and interest earned.

What does the 'a' in the general formula for exponential functions represent?

• Decay rate

• Growth rate

• Initial value

• Time

What does the exponent 'X' typically represent in the formula for exponential functions?

• Time or other units

• Final value

• Growth or decay rate

• Initial value

For exponential growth, the rate (B) must be:

• Equal to 0

• Greater than 1

• Less than 1

• Equal to 1

What is the initial value in the population growth example?

• 1,500

• 5,000

• 10,000

• 64

In the context of exponential decay, what does a decay rate between 0 and 1 signify?

• The function remains constant

• The function will reset to its initial value

• The function will decrease over time

• The function will increase over time

What is the decay rate for the basketball tournament example?

• 1.05

• 1.5

• 0.5

• 0.12

After 3 years, how much will a $19,000 car depreciate at a rate of 12% per year?

• $12,947.97

• $10,000.00

• $15,000.00

• $17,000.00

How much will the car be worth after 3 years, given a 12% depreciation rate per year?

• $18,000.00

• $16,000.00

• $12,947.97

• $14,000.00

What is the growth rate for Bethany's savings account?

• 105.25%

• 5.25%

• 5%

• 1.0525

How much interest has Bethany earned after 25 years?

• $5,000.00

• $12,968.95

• $17,968.95

• $15,000.00