Writing Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent, typically in the form of y = a * b^x, where a is a constant, b is the base, 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 number that is raised to a power. In the equation y = a * b^x, b is the base.

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, meaning as x increases, y 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, meaning as x increases, y decreases.

Tags

CCSS.HSF-IF.C.7E

Front

How do you write an exponential equation from a word problem?

Back

Identify the initial value and the growth/decay factor, then use the form y = a * b^x, where a is the initial value and b is the growth/decay factor.

Tags

CCSS.HSF.LE.A.2

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^x, where a is the initial amount, b is the base (growth/decay factor), and x is the exponent.

Front

How can you determine the growth factor in an exponential equation?

Back

The growth factor is the base (b) in the equation y = a * b^x. If b > 1, it indicates growth; if 0 < b < 1, it indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the initial value in an exponential equation?

Back

The initial value (a) represents the starting amount before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x, then draw a smooth curve that approaches the x-axis but never touches it.

Tags

CCSS.HSF-IF.C.7E