Comparing Quadratic and Exponential Functions: IM Alg1.6.4
[url=https://im.kendallhunt.com/HS/teachers/1/6/4/preparation.html]“Comparing Quadratic and Exponential Functions”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.6.4 Lesson
- IM Alg1.6.4 Lesson: Comparing Quadratic and Exponential Functions
- Alg1.6.4 Practice
- IM Alg1.6.4 Practice: Comparing Quadratic and Exponential Functions
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.
[list][size=150][*]In Pattern A, the length and width of the rectangle grow by one small square from each step to the next.[/*][*]In Pattern B, the number of small squares doubles from each step to the next.[br][/*][*]In each pattern, the number of small squares is a function of the step number, [math]n[/math].[/*][/size][/list][br][table][tr][td][size=150]Pattern A[/size][/td][td][size=150]Pattern B[/size][/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][br][br][size=150]Write an equation to represent the number of small squares at Step [math]n[/math] in Pattern A.[/size][br]
Is the function linear, quadratic, or exponential?[br]
[size=150]Write an equation to represent the number of small squares at Step [math]n[/math] in Pattern B.[br][/size]
Is the function linear, quadratic, or exponential?[br]
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:
[math]p\left(x\right)=6x^2[/math] and [math]q\left(x\right)=3^x[/math].[br][br]Investigate the output of [math]p[/math] and [math]q[/math] for different values of [math]x[/math]. For large enough values of [math]x[/math], one function will have a greater value than the other. Which function will have a greater value as [math]x[/math] increases?
Support your answer with tables, graphs, or other representations.
Jada says that some exponential functions grow more slowly than the quadratic function as [math]x[/math] increases. Do you agree with Jada? Explain your reasoning.[br]
Could you have an exponential function [math]g\left(x\right)=b^x[/math] so that [math]g(x)[/math]<[math]f(x)[/math] for all values of [math]x[/math].
IM Alg1.6.4 Practice: Comparing Quadratic and Exponential Functions
[size=150]The table shows values of the expressions [math]10x^2[/math] and [math]2^x[/math]. [/size][br][br]Describe how the values of each expression change as [math]x[/math] increases.
[size=150]Predict which expression will have a greater value when:[br][/size][br][math]x[/math] is 8
[math]x[/math] is 10
[math]x[/math] is 12
Find the value of each expression when [math]x[/math] is 8, 10, and 12 and fill out the table.[br][br]Make an observation about how the values of the two expressions change as [math]x[/math] becomes greater and greater.
[size=150]Function [math]f[/math] is defined by [math]f(x)=1.5^x[/math]. Function [math]g[/math] is defined by [math]g\left(x\right)=500x^2+345x[/math].[/size][br][br]Which function is quadratic? Which one is exponential?[br]
The values of which function will eventually be greater for larger and larger values of [math]x[/math]?[br]
[size=150]Create a table of values to show that the exponential expression [math]3\left(2\right)^x[/math] eventually overtakes the quadratic expression [math]3x^2+2x[/math].[/size]
[size=150]The table shows the values of [math]4^x[/math] and [math]100x^2[/math] for some values of [math]x[/math].[/size][br][br][img]data:image/png;base64,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[/img][br][br]Use the patterns in the table to explain why eventually the values of the exponential expression [math]4^x[/math] will overtake the values of the quadratic expression [math]100x^2[/math].
Here is a pattern of shapes. The area of each small square is 1 sq cm.
[img]data:image/png;base64,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[/img][br][br]What is the area of the shape in Step 10?[br]
What is the area of the shape in Step [math]n[/math]?[br]
Explain how you see the pattern growing.[br]
[size=150]A bicycle costs $240 and it loses [math]\frac{3}{5}[/math] of its value each year.[/size][br][br]Write expressions for the value of the bicycle, in dollars, after 1, 2, and 3 years.[br]
When will the bike be worth less than $1?[br]
Will the value of the bike ever be 0? Explain your reasoning.[br]
[size=150]A farmer plants wheat and corn. It costs about $150 per acre to plant wheat and about $350 per acre to plant corn. The farmer plans to spend no more than $250,000 planting wheat and corn. The total area of corn and wheat that the farmer plans to plant is less than 1200 acres.[/size][br][br][img]data:image/png;base64,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[/img][br][br][size=150]This graph represents the inequality, [math]150w+350c\le250,000[/math], which describes the cost constraint in this situation. Let [math]w[/math] represent the number of acres of wheat and [math]c[/math] represent the number of acres of corn. [/size][br][br]The inequality, [math]w + c < 1,\!200[/math] represents the total area constraint in this situation. On the same coordinate plane, graph the solution to the inequality you wrote.
Use the graphs to find at least two possible combinations of the number of acres of wheat and the number of acres of corn that the farmer could plant.
The combination of 400 acres of wheat and 700 acres of corn meets one constraint in the situation but not the other constraint. Which constraint does this meet? Explain your reasoning.