Writing Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, y = a * b^x, where a and b are constants.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a constant, b is the base (b > 0, b ≠ 1), and x is the exponent.

Front

How do you identify the base in an exponential equation?

Back

The base in an exponential equation is the constant that is raised to the power of the variable. For example, in y = 3 * 2^x, the base is 2.

Front

What does it mean for an exponential function to be increasing?

Back

An exponential function is increasing if the base (b) is greater than 1. This means that as x increases, f(x) also increases.

Tags

CCSS.HSF-IF.C.7E

Front

What does it mean for an exponential function to be decreasing?

Back

An exponential function is decreasing if the base (b) is between 0 and 1. This means that as x increases, f(x) decreases.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is a real-world example of exponential growth?

Back

A real-world example of exponential growth is population growth, where the population increases at a rate proportional to its current size.

Tags

CCSS.HSF-LE.A.1A

Front

What is a real-world example of exponential decay?

Back

A real-world example of exponential decay is radioactive decay, where the quantity of a radioactive substance decreases over time.