Comparing Quadratic and Exponential Functions

ID: karih-rimug
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
Standards: 6.EE.A.1HSF-LE.A.3HSF-BF.A.1.aHSF-IF.C
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26 questions

Comparing Quadratic and Exponential Functions

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From Least to Greatest

1) List these quantities in order, from least to greatest, without evaluating each expression.

A. 2102^{10} \quad \quad B. 10210^2 \quad \quad C. 292^9 \quad \quad D. 929^2 \quad \quad

2) Explain your reasoning.

Which One Grows Faster?

Here is Pattern A.

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

The number of small squares is a function of the step number, nn.

A template for answering this question. Ask your instructor for an alternative.

3) Write an equation to represent the number of small squares at Step nn in Pattern A.

4) Is the function linear, quadratic, or exponential?

Determine f(n)f(n), number of small squares, given the step number, nn.

5) n = 0n \ = \ 0

Show Work

6) n = 1n \ = \ 1

Show Work

7) n = 2n \ = \ 2

Show Work

8) n = 3n \ = \ 3

Show Work

9) n = 4n \ = \ 4

Show Work

10) n = 5n \ = \ 5

Show Work

11) n = 6n \ = \ 6

Show Work

12) n = 7n \ = \ 7

Show Work

13) n = 8n \ = \ 8

Show Work

Here is Pattern B.

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

The number of small squares is a function of the step number, nn.

A template for answering this question. Ask your instructor for an alternative.

14) Write an equation to represent the number of small squares at Step nn in Pattern B.

15) Is the function linear, quadratic, or exponential?

Determine g(n)g(n), number of small squares, given the step number, nn.

16) n = 0n \ = \ 0

Show Work

17) n = 1n \ = \ 1

Show Work

18) n = 2n \ = \ 2

Show Work

19) n = 3n \ = \ 3

Show Work

20) n = 4n \ = \ 4

Show Work

21) n = 5n \ = \ 5

Show Work

22) n = 6n \ = \ 6

Show Work

23) n = 7n \ = \ 7

Show Work

24) n = 8n \ = \ 8

Show Work

25) How would the two patterns compare if they continue to grow? Make 1–2 observations.

Comparing Two More Functions

26) Here are two functions: p(x)=6x2p(x) = 6x^2 and q(x)=3xq(x) = 3^x.

Investigate the output of pp and qq for different values of xx. For large enough values of xx, one function will have a greater value than the other. Which function will have a greater value as xx increases?

Support your answer with tables, graphs, or other representations.