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.

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.

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.

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.

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.

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.

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.