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Unit 4, Lesson 4

Comparing Quadratic and Exponential Functions

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Integrated Math 2

Practice

Problem 1

The table shows values of the expressions $10x^2$ and $2^x$.

Describe how the values of each expression change as $x$ increases.
Complete the table.
Make an observation about how the values of the two expressions change as $x$ becomes greater and greater.

$x$	$10x^2$	$2^x$
1	10	2
2	40	4
3	90	8
4	160	16
8
10
12

Problem 2

Function $f$ is defined by $f(x)=1.5^x$. Function $g$ is defined by $g(x)=500x^2 + 345x$.

Which function is quadratic? Which one is exponential?
The values of which function will eventually be greater for larger and larger values of $x$?

Problem 4

The table shows the values of $4^x$ and $100x^2$ for some values of $x$.

Use the patterns in the table to explain why eventually the values of the exponential expression $4^x$ will overtake the values of the quadratic expression $100x^2$.

$x$	$4^x$	$100x^2$
1	4	100
2	16	400
3	64	900
4	256	1600
5	1024	2500

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