IM Alg1.6.4 Lesson: Comparing Quadratic and Exponential Functions
List these quantities in order, from least to greatest, without evaluating each expression. Be prepared to explain your reasoning.
Write an equation to represent the number of small squares at Step in Pattern A.
Pattern A Pattern B 
Is the function linear, quadratic, or exponential?
Write an equation to represent the number of small squares at Step in Pattern B.
Is the function linear, quadratic, or exponential?
Complete the table where f represents Pattern A and g represents Pattern B.
How would the two patterns compare if they continue to grow? Make 1–2 observations.
Here are two functions:
and . Investigate the output of and for different values of . For large enough values of , one function will have a greater value than the other. Which function will have a greater value as increases?
Support your answer with tables, graphs, or other representations.
Jada says that some exponential functions grow more slowly than the quadratic function as increases. Do you agree with Jada? Explain your reasoning.
Could you have an exponential function so that < for all values of .