Understanding Exponential Growth Functions

This lesson covers exponential growth functions, focusing on the rate of change by examining equal factors over equal intervals. It explains the equation for exponential growth, the role of exponents, and how to graph these functions using tables. The lesson explores functions with different bases, such as 2, 3, and 4, and highlights the rapid increase in values. The key takeaway is understanding that exponential growth involves equal factors over equal intervals, leading to a rapid increase in function values.

What is the base in the exponential growth function f(x) = 2^x?

• x

• y

• 2

• f(x)

When graphing the function f(x) = 2^x, what happens to f(x) each time x increases by 1?

• It decreases

• It doubles

• It remains the same

• It triples

In the function f(x) = 3^x, what is the value of f(x) when x is 0?

• 0

• 9

• 1

• 3

What does each increase in the power of x by 1 represent in the function f(x) = 3^x?

• Dividing by 3

• Adding 3

• Multiplying by 3

• Subtracting 3

What is the base in the exponential function f(x) = 4^x?

• 4

• x

• f(x)

• y

How does the graph of f(x) = 4^x compare to f(x) = 2^x and f(x) = 3^x?

• More steep

• Flat

• Equally steep

• Less steep

What is a common characteristic of exponential growth functions?

• They have a constant rate of change

• They are linear

• They decrease over time

• Equal intervals have equal factors