7.4.2 Exploring Linear, Exponential, and Quadratic Growth

In this activity, you will compare two different patterns. In each pattern, the number of small squares is a function of the step number, $n$.

1. In Pattern A, the length and width of the rectangle grow by 1 small square from each step to the next.

Pattern A

2. In Pattern B, the number of small squares doubles from each step to the next.

Pattern B

Additional Resources

Determining Growth Factors

Is the pattern below represented by a function that is linear, exponential, or quadratic?

Step 1 - Draw a table. In the right column, determine the growth factor.

Step Number$x$	Number of Squares$f(x)$	Growth Factor
$0$	$1$	$3$
$1$	$3$	$3$
$2$	$9$	$3$
$3$	$27$	$3$

Step 2 - Write the function to represent the pattern.

$f(x)=3^x$

Step 3 - Determine what type of function this is.

The function is exponential.

Try it

Determining Growth Factors

Is the pattern below represented by a function that is linear, exponential, or quadratic?

Here is how to use the growth factor to determine if this pattern is represented by a linear, quadratic, or exponential function:

Step 1 - Create a table and determine the growth factor.

Step Number$x$	Number of Squares$f(x)$	Growth Factor
$0$	$0$
$1$	$3$
$2$	$12$	$4$
$3$	$27$	$2.25$

Step 2 - Determine the function.

$f(x)=3x^2$

Step 3 - Determine what type of function this is.

This is a quadratic function. The growth rate changes between each step.