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 a positive real number, and 'x' is the exponent.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals 'a'.

Front

Identify the y-intercept of the function f(x) = 5(3)^x.

Back

The y-intercept is 5.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant and 'b' is a positive real number.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where 'b' > 1.

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

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.

Front

If f(x) = 10(2)^x, what is the initial value?

Back

The initial value is 10.

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 1) results in slower growth.