Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What does the base of an exponential function represent?

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

Write the exponential function for the following table: (1, 2), (2, 4), (3, 8)

Back

f(x) = 1(2^x)

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the function increases rapidly as 'x' increases, while exponential decay occurs when the function decreases rapidly as 'x' increases.

Front

Identify the function that represents exponential decay: y = 5(0.5)^x or y = 5(2)^x

Back

y = 5(0.5)^x represents exponential decay.

Front

What is the general form of an exponential growth function?

Back

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

Front

If f(x) = 3(2^x), what is f(3)?

Back

f(3) = 3(2^3) = 3(8) = 24.

Front

What does it mean if a function is described as having a variable exponent?

Back

It means that the exponent in the function is not a constant but a variable, which is characteristic of exponential functions.

Front

Write an equation that models the data shown: (1, 6), (2, 12), (3, 24)

Back

y = 6(2^x)