Exponential Functions

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 the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function represents the initial value of the function when x = 0.

Front

How do you identify the growth factor in an exponential function?

Back

The growth factor 'b' in an exponential function f(x) = a(b)^x is the base 'b' when 'b' > 1.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Front

If f(x) = 3(2)^x, what is the y-intercept?

Back

The y-intercept is 3.

Front

In the function f(x) = 5(0.5)^x, is it an example of growth or decay?

Back

It is an example of exponential decay.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(b)^x, where 0 < b < 1.

Front

How can you determine if a function is increasing or decreasing?

Back

A function is increasing if the base 'b' is greater than 1 and decreasing if the base 'b' is between 0 and 1.

Front

What is the formula to find the y-intercept of the function f(x) = 7(3)^x?

Back

The y-intercept is found by evaluating f(0), which gives f(0) = 7(3)^0 = 7.

Front

What does the term 'initial value' refer to in an exponential function?

Back

The initial value refers to the y-intercept of the function, which is the value of the function when x = 0.