Exponential Functions and Their Properties

The video tutorial explains exponential functions, focusing on how the base affects growth or decay. A base of one results in no change, while a base greater than one leads to growth, and a base less than one causes decay. The tutorial also covers rewriting the base to determine the rate of change and provides examples to illustrate these concepts.

What does the base of an exponential function indicate?

• The initial value of the function

• The exponent value

• The rate of growth or decay

• The constant value of the function

If the base of an exponential function is 1, what happens to the quantity?

• It grows exponentially

• It decays exponentially

• It remains constant

• It oscillates

What happens to an exponential function when the base is greater than one?

• The function decays

• The function remains constant

• The function grows

• The function oscillates

In an exponential function with a base less than one, what occurs as the exponent increases?

• The quantity grows

• The quantity decays

• The quantity oscillates

• The quantity remains constant

How can the base of an exponential function be rewritten to show the rate of change?

• As a logarithm

• As 1 + r or 1 - r

• As a derivative

• As a constant

What does the 'r' represent in the rewritten form 1 + r?

• The exponent

• The base

• The initial value

• The rate of change

In the function y = 3^x, what is the rate of change when rewritten as 1 + 2?

• 100%

• 200%

• 75%

• 50%

How can the base 0.5 be rewritten to show a decrease in quantity?

• 1 - 0.25

• 1 + 0.25

• 1 - 0.5

• 1 + 0.5

What does a base of 0.25 indicate about the rate of change?

• The quantity decreases by 75%

• The quantity remains constant

• The quantity increases by 75%

• The quantity increases by 25%

If a function is rewritten as 1 - 0.75, what does this indicate?

• The function grows by 75%

• The function decays by 75%

• The function remains constant

• The function grows by 25%