In this activity, you will compare two different patterns. In each pattern, the number of small squares is a function of the step number, .
1. In Pattern A, the length and width of the rectangle grow by 1 small square from each step to the next.
Pattern A
a. Write an equation to represent the number of small squares at Step in Pattern A.
Compare your answer:
b. Is the function in Pattern A linear, quadratic, or exponential?
It is quadratic.
c. Complete the table for Pattern A.
Step Number | Number of Small Squares |
Compare your answers:
Step Number | Number of Small Squares |
2. In Pattern B, the number of small squares doubles from each step to the next.
Pattern B
a. Write an equation to represent the number of small squares at Step in Pattern B.
Compare your answer:
b. Is the function in Pattern B linear, quadratic, or exponential?
It is exponential.
c. Complete the table for Pattern B.
Step Number | Number of Small Squares |
Compare your answers:
Step Number | Number of Small Squares |
3. How would the two patterns compare if they continue to grow? Make one to two observations.
Compare your answer:
The number of small squares in Pattern B grows much more quickly than the number of squares in Pattern A once is greater than . The patterns have the same number of squares when and when .
Self Check
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 | Number of Squares | Growth Factor |
Step 2 - Write the function to represent the pattern.
Step 3 - Determine what type of function this is.
The function is exponential.
Try it
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 | Number of Squares | Growth Factor |
Step 2 - Determine the function.
Step 3 - Determine what type of function this is.
This is a quadratic function. The growth rate changes between each step.