Exponential Functions and Decay Concepts

The video tutorial by Mr. Bean covers exponential decay, contrasting it with exponential growth. It begins with a review of geometric sequences and transitions into definitions and examples of exponential growth and decay. The tutorial explains how to graph these functions and calculate percent increases and decreases. Finally, it applies these concepts to solve real-world word problems, emphasizing the importance of understanding exponential functions in various contexts.

What is the first number in the geometric sequence discussed in the introduction?

• 24

• 6

• 12

• 48

In a geometric sequence, if the first term is 12 and the common ratio is 2, what is the third term?

• 24

• 48

• 36

• 12

What is the base of the exponent in the sequence where numbers are halved each time?

• 2

• 1/2

• 3

• 1/3

If a sequence starts at 12 and halves each time, what is the fourth term?

• 0.75

• 6

• 3

• 1.5

What is the condition for exponential growth in terms of the base of the exponent?

• Base < 1

• Base > 1

• Base = 0

• Base = 1

Which of the following represents exponential decay?

• Base > 1

• Base < 1

• Base = 1

• Base = 0

In the function f(x) = 2 * (7/5)^x, what does the base 7/5 indicate?

• Exponential growth

• Exponential decay

• Linear growth

• Linear decay

For the function f(x) = 4/3 * (1/6)^x, what does the base 1/6 indicate?

• Linear decay

• Linear growth

• Exponential decay

• Exponential growth

What is the base of the exponent in the function f(x) = 1/5 * (4/3)^x?

• 1/5

• 4/3

• 1/3

• 5/4

When graphing exponential functions, what is the initial step?

• Calculate the derivative

• Find the slope

• Determine the asymptote

• Plot the y-intercept