Exponential Functions

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 is the general form of an exponential growth function?

Back

The general form is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(b^x) where 0 < b < 1.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' determines the rate of growth or decay; if b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

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

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.

Front

What is the y-intercept of y = 3(4^x)?

Back

The y-intercept is 3.

Front

What is the y-intercept of y = 4^(x+1)?

Back

The y-intercept is (0, 4).

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the function increases rapidly (b > 1), while exponential decay occurs when the function decreases rapidly (0 < b < 1).

Front

How can you identify if a function is linear or exponential?

Back

A linear function has a constant rate of change, while an exponential function has a variable rate of change that increases or decreases exponentially.

Front

What is the graph of an exponential growth function like?

Back

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