Parts of Exponential Functions - 12/2/24

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the value of a function increases at a rate proportional to its current value, typically represented by a base greater than 1 in the function f(x) = a(b)^x.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the value of a function decreases at a rate proportional to its current value, typically represented by a base between 0 and 1 in the function f(x) = a(b)^x.

Front

Identify the base in the function f(x) = 2(3)^x.

Back

The base is 3.

Front

What is the y-intercept of the function f(x) = 5(2)^x?

Back

The y-intercept is 5.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base 'b' in f(x) = a(b)^x is greater than 1, it is exponential growth. If 'b' is between 0 and 1, it is exponential decay.

Front

What is the initial value in the function f(x) = 4(5)^x?

Back

The initial value is 4.

Front

What is the common ratio in the function f(x) = 3(2)^x?

Back

The common ratio is 2.

Front

If f(x) = 7(0.5)^x, what type of function is this?

Back

This is an example of exponential decay.

Front

What does the term 'exponential function' imply about the rate of change?

Back

The rate of change of an exponential function increases or decreases rapidly, depending on whether it is growth or decay.