Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. It can be expressed in the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

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

Back

A function exhibits exponential growth when the base (b) is greater than 1 (b > 1). This means that as x increases, the value of f(x) increases rapidly.

Front

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

Back

A function exhibits exponential decay when the base (b) is between 0 and 1 (0 < b < 1). This means that as x increases, the value of f(x) decreases rapidly.

Front

Identify the common ratio in the function f(x)=2(4)^x.

Back

The common ratio is 4.

Front

If f(x) = 2(1/7)^x, what type of function is this?

Back

This is an exponential decay function.

Front

What is the common ratio if the f(x) values are being divided by 3?

Back

The common ratio is 1/3.

Front

What values of b make an exponential growth function?

Back

b > 1.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where a is a constant and b is the base.

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 b is a positive constant.

Front

What is the difference between exponential growth and exponential decay?

Back

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