Exponential Functions (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.

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(b^x) where 0 < b < 1.

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept of an exponential function can be found by evaluating the function at x = 0, which gives y = a(b^0) = a.

Front

What is the y-intercept of the function y = 3(2^x)?

Back

The y-intercept is (0, 3), since y = 3(2^0) = 3.

Front

What is the y-intercept of the function y = 3(½)^x?

Back

The y-intercept is (0, 3), since y = 3(½^0) = 3.

Front

What does it mean for a graph to show exponential growth?

Back

A graph shows exponential growth if it rises rapidly as x increases, indicating that the function's value increases at an increasing rate.

Front

What does it mean for a graph to show exponential decay?

Back

A graph shows exponential decay if it falls rapidly as x increases, indicating that the function's value decreases at a decreasing rate.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth can be identified on a graph by a curve that rises steeply to the right.