Exponential Functions and Decay Rates

The video tutorial explains the concepts of decay factor and decay rate in exponential functions. It provides an example of a decaying exponential function, where the decay factor is less than one, leading to a decrease in value. The tutorial demonstrates how to calculate new values using the decay factor and explains the relationship between decay factor and decay rate. The decay rate is defined as one minus the decay factor, indicating the percentage decrease. The video concludes with a recap and comparison of growth and decay factors and rates, emphasizing their roles in exponential functions.

What is the decay factor in an exponential function?

• The initial value of the function

• The rate at which the function grows

• The base of the exponential function

• The percentage by which the function decreases

Why is the function described as a decaying exponential function?

• Because the initial value is greater than 10

• Because the function increases over time

• Because the decay rate is more than 50%

• Because the decay factor is less than one

What is the initial value when X is zero in the given example?

• 10

• 0.8

• 6.4

• 8

How much does the value decrease from 10 to 8?

• By 10%

• By 30%

• By 40%

• By 20%

What happens to the value when it decreases by 20%?

• It increases by 20%

• It decreases by 20% of the previous value

• It doubles

• It remains the same

What is the formula for calculating the decay rate?

• Decay Factor times Initial Value

• Decay Factor minus 1

• 1 minus the Decay Factor

• Initial Value divided by Decay Factor

What is the new value when the previous value is 8 and the decay factor is 0.80?

• 8.8

• 9.6

• 7.2

• 6.4

What is the decay rate if the decay factor is 0.80?

• 30%

• 20%

• 40%

• 10%

How do you calculate the next value in a decaying exponential function?

• Divide the previous value by the decay rate

• Multiply the previous value by the decay factor

• Add the decay rate to the previous value

• Subtract the decay factor from the previous value

How is the decay factor related to the decay rate?

• Decay rate is the decay factor minus one

• Decay rate is the decay factor plus one

• Decay rate is the square of the decay factor

• Decay rate is one minus the decay factor