12/5 Exponential Graphs

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b)^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It describes growth or decay processes.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base b > 1, leading to an increase in value as x increases. Exponential decay occurs when the base 0 < b < 1, leading to a decrease in value as x increases.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a(b)^x is the point where x = 0, which is (0, a).

Front

How do you identify an exponential growth function from its equation?

Back

An exponential growth function can be identified by its equation y = a(b)^x where b > 1.

Front

How do you identify an exponential decay function from its equation?

Back

An exponential decay function can be identified by its equation y = a(b)^x where 0 < b < 1.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = a(b)^x, where a is a constant and b is the base.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth factor (if b > 1) or decay factor (if 0 < b < 1) of the function.

Front

What is the significance of the constant 'a' in an exponential function?

Back

The constant 'a' in an exponential function y = a(b)^x represents the initial value or the y-intercept of the graph.

Front

How can you determine the y-intercept from an exponential equation?

Back

To determine the y-intercept from an exponential equation y = a(b)^x, substitute x = 0. The y-intercept is (0, a).

Front

What is the graphical representation of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the x-axis to the left, never touching it.