How can I understand the exponential growth from the graph?

The exponential kinda does like a half of an u shape. Just like one side, now if you had both sides though it would be a full u shape

It's Exponential because the number increases and it is always being multiplied by 2

Yep, linear gets numbers added to it. Another good way to remember it's exponential s if the variable is in the exponents, and only in the exponents.

isn't it the same as geometric sequences?

They are related, but not the same. Remember that a sequence is not continuous, it has values only at whole numbers generally starting at 1, 2, 3, 4 so it is a bunch of dots on the graph. If you have the exponential function that is related to the sequence, it is continuous and goes from negative infinity to infinity.

x|0,1, 2, 3 y|2,6,18,54 How is this exponential?

The equation would be 2*3^x. Ex. 2*3^0=2*1=2; 2*3^1=2*3=6; 2*3^2=2*9=18. Each increase is by a power of 3.

Which characteristic makes a table exponential and which one makes linear?

Linear is when you adding and when you multiply the exponential.

is subtracting or negative considered linear

subtracting the same number over and over is linear.

Main content

Algebra 1

Course: Algebra 1 > Unit 12

Lesson 1: Exponential vs. linear growth

Warmup: exponential vs. linear growth

CCSS.Math:

Exponential vs. linear growth: review

Linear and exponential relationships differ in the way the y-values change when the x-values increase by a constant amount:

In a linear relationship, the y-values have equal differences.
In an exponential relationship, the y-values have equal ratios.

Let's see some examples

Example 1: Linear growth

Consider the relationship represented by this table:

x	12	15	18	21
y	minus, 2	5	12	19

Here, the x-values increase by exactly 3 units each time,

x		\curvearrowright, plus, 3		\curvearrowright, plus, 3		\curvearrowright, plus, 3
	12		15		18		21

and the y-values increase by a constant difference of 7.

y		\curvearrowright, plus, 7		\curvearrowright, plus, 7		\curvearrowright, plus, 7
	minus, 2		5		12		19

Therefore, this relationship is linear because each y-value is 7 more than the value before it.

Example 2: Exponential growth

Consider the relationship represented by this table:

x	0	1	2	3
y	1	3	9	27

Here, the x-values increase by exactly 1 unit each time,

x		\curvearrowright, plus, 1		\curvearrowright, plus, 1		\curvearrowright, plus, 1
	0		1		2		3

and the y-values increase by a constant factor of 3.

y		\curvearrowright, times, 3		\curvearrowright, times, 3		\curvearrowright, times, 3
	1		3		9		27

Therefore, this relationship is exponential because each y-value is 3 times the value before it.

Example 3: Growth that is neither linear nor exponential

It's important to remember there can be many relationships that describe growth but aren't linear or exponential.

For example, consider the relationship represented by this table:

x	2	4	6	8
y	4	9	16	25

Here, the x-values increase by exactly 2 units each time.

x		\curvearrowright, plus, 2		\curvearrowright, plus, 2		\curvearrowright, plus, 2
	2		4		6		8

However, the differences between the y-values aren't constant,

y		\curvearrowright, plus, 5		\curvearrowright, plus, 7		\curvearrowright, plus, 9
	4		9		16		25

and the ratios aren't constant either.

y		\curvearrowright, times, start fraction, 9, divided by, 4, end fraction		\curvearrowright, times, start fraction, 16, divided by, 9, end fraction		\curvearrowright, times, start fraction, 25, divided by, 16, end fraction
	4		9		16		25

Therefore, this relationship is neither linear nor exponential.

Check your understanding

Problem 1

x	0	1	2	3
y	5	10	15	20

Fill in the blanks.

This relationship is

because each y-value is

the value before it.

Problem 2

x	0	1	2	3
y	2	6	18	54

Fill in the blanks.

This relationship is

because each y-value is

the value before it.

Problem 3

Fill in the blanks.

This relationship is

because each y-value is

the value before it.

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Karra Wallis
Posted 3 years ago. Direct link to Karra Wallis's post “x|0,1, 2, 3 y|2,6,18,54 H...”
x|0,1, 2, 3
y|2,6,18,54
How is this exponential?
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- Bob Sheehy
  Posted 3 years ago. Direct link to Bob Sheehy's post “The equation would be 2*3...”
  The equation would be 2*3^x. Ex. 2*3^0=2*1=2; 2*3^1=2*3=6; 2*3^2=2*9=18. Each increase is by a power of 3.
  Comment on Bob Sheehy's post “The equation would be 2*3...”
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ebell813
Posted 3 years ago. Direct link to ebell813's post “It's Exponential because ...”
It's Exponential because the number increases and it is always being multiplied by 2
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(8 votes)
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- loumast17
  Posted 3 years ago. Direct link to loumast17's post “Yep, linear gets numbers ...”
  Yep, linear gets numbers added to it. Another good way to remember it's exponential s if the variable is in the exponents, and only in the exponents.
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Mohammad Hadi
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How can I understand the exponential growth from the graph?
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- Morgan Kling
  Posted 3 years ago. Direct link to Morgan Kling's post “The exponential kinda doe...”
  The exponential kinda does like a half of an u shape. Just like one side, now if you had both sides though it would be a full u shape
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Wow, how the heck do you guys stand this every minute of every day?
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- Me
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  They don’t.
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Vinay Sharma
Posted 2 years ago. Direct link to Vinay Sharma's post “isn't it the same as geom...”
isn't it the same as geometric sequences?
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- David Severin
  Posted 2 years ago. Direct link to David Severin's post “They are related, but not...”
  They are related, but not the same. Remember that a sequence is not continuous, it has values only at whole numbers generally starting at 1, 2, 3, 4 so it is a bunch of dots on the graph. If you have the exponential function that is related to the sequence, it is continuous and goes from negative infinity to infinity.
  Comment on David Severin's post “They are related, but not...”
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dc4369934
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Why? This makes me wanna cry myself to sleep.
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- 508344
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  I know it's hard.
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02-26 Tadic, Stevana
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is subtracting or negative considered linear
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- David Severin
  Posted 4 years ago. Direct link to David Severin's post “subtracting the same numb...”
  subtracting the same number over and over is linear.
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Morgan717
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How do I get answers? It's confusing
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i dont know the last one
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Mr. Zuniga
Posted 8 months ago. Direct link to Mr. Zuniga's post “Which characteristic make...”
Which characteristic makes a table exponential and which one makes linear?
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- Yazmin Martinez
  Posted 8 months ago. Direct link to Yazmin Martinez's post “Linear is when you adding...”
  Linear is when you adding and when you multiply the exponential.
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