Is there a difference between exponential and geometric functions?

In the case that when you say "geometric function", you are referring to a function that represents a geometric sequence, the function that represents an exponential function would look like this: f(x) = ab^x, while a geometric function would look like this: ab^x-1. Additionally, in a geometric function, the domain is any integer value that is greater than or equal to 1, while in an exponential function, the domain is all real numbers. This can make sense if you think about the fact that you cannot have a negative first or a two and a half term in a sequence of numbers.

What is the decay factor in the exponential decay function y=a(1−r)t ?

The decay factor is the (1-r) part. Since r is a percent we subtract it from 1 to find how much is left after one round. For instance if you have 100 cookies and you eat 10% every minute, after 1 minute how many would you have? We take the number we have and multiply by 90% to find how much is left (1 - .1 = 0.9 which is 90%) 100*(1-0.1)^1 100*0.9 = 90 cookies So, unlike in growth functions where we *ADD* the rate to 1, *in decay we SUBTRACT the rate from 1*

can a growth factor be negative

Good question! It turns out that the answer for that is no, not really... If the growth factor is negative, then for non-integer values of `x`, we would be raising a *negative number* to a fractional power, which does not result in a real number. For an exponential function with negative growth factor, the domain is limited to integer values of `x`. This issue does not occur when the growth factor is positive, since you can plug in any positive number raised to a fractional power. Here's an exercise: Plug in the values of `(-2)^(0.5)` and `(2)^(0.5)` into a _regular calculator_. Only the `(-2)^(0.5)` would result in a math error. Happy learning.

hello so i have 2 questions: 1) isnt linear and exponential function same as arithmetic and geometric sequences? 2) can an exponential function say grow till it stops at f(x) = 50 for example? or an exponential decay that stops at f(x) = -50? or does every exponential function never stop?

1) Yes. They are the same. But when you are describing a sequence rather than a function in general, you will use arithmetic and geometric instead. 2) Yes and no. It can *tend* to a value like 50, but never reaches it. For example f(x) = 2^x. It cannot reach 0, but you would say when x reaches negative infinity, f(x) = 0.

Main content

Course: Algebra 1 > Unit 12

Lesson 7: Exponential vs. linear models

Exponential growth & decay: FAQ

Google Classroom

Frequently asked questions about exponential growth & decay

What's the difference between exponential and linear growth?

In linear growth, we add or subtract the same amount each time period, while in exponential growth, we multiply by the same factor each time period. For example, linear growth might involve adding

5

each day, while exponential growth might involve multiplying by

2

each day.

Practice with our Exponential vs. linear growth exercise.

How can we tell if a graph represents exponential or linear growth?

One of the hallmarks of exponential growth is that the graph will get steeper and steeper over time. Linear growth, on the other hand, will have a constant slope.

Practice with our Graphs of exponential growth exercise.

What's the difference between exponential growth and exponential decay?

While both involve exponential functions, exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.

Practice with our Exponential growth vs. decay exercise.

How do we create an exponential function from a table or graph?

There are a few steps to this. First, identify the initial value (the

y

-intercept). Second, determine whether the function is growing or decaying. Third, find the growth or decay factor - this will be the number we're multiplying by each time period. Once we have these three pieces of information, we can write the exponential function in the form

y = a (b)^{x}

, where

a

is the initial value and

b

is the growth or decay factor.

Practice with our Exponential functions from tables & graphs exercise.

Where do we see exponential growth and decay in the real world?

There are many examples! Compound interest is a common example of exponential growth, while radioactive decay is a common example of exponential decay.

Practice with our Connecting exponential graphs with contexts exercise.

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squirrel497
Posted a year ago. Direct link to squirrel497's post “Is there a difference bet...”
Is there a difference between exponential and geometric functions?
Button navigates to signup pageComment on squirrel497's post “Is there a difference bet...”
(7 votes)
Answer
- Khan Academy user
  Posted a year ago. Direct link to Khan Academy user's post “In the case that when you...”
  In the case that when you say "geometric function", you are referring to a function that represents a geometric sequence, the function that represents an exponential function would look like this: f(x) = ab^x, while a geometric function would look like this: ab^x-1. Additionally, in a geometric function, the domain is any integer value that is greater than or equal to 1, while in an exponential function, the domain is all real numbers. This can make sense if you think about the fact that you cannot have a negative first or a two and a half term in a sequence of numbers.
  Button navigates to signup page
  (15 votes)
sarra
Posted 9 months ago. Direct link to sarra's post “this is the most confusin...”
this is the most confusing lesson I've had on this site
someone said it evolves things you learn in algebra 2
but we're in algebra 1 for a reason
Button navigates to signup pageComment on sarra's post “this is the most confusin...”
(4 votes)
Answer
- ryan
  Posted 8 months ago. Direct link to ryan's post “So for me the biggest stu...”
  So for me the biggest stumbling block was the common factor. What clicked - again, for me - was focusing on getting the # we multiply by with a simple equation. My first question was initial value of 4, and the next dot was 7,1. I jotted: 4x=7 (the x being more a multiplication sign in my head here). As in, 4 times what gets me to a Y value of 7? Divide 4 from each side and we x=7/4, which is what the hint/answer has for the common factor. Hope this helps anyone... as I am clawing my way through this unit slowly...
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ibailey
Posted 3 months ago. Direct link to ibailey's post “What is the decay factor ...”
What is the decay factor in the exponential decay function y=a(1−r)t
?
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(2 votes)
Answer
- FreeRadical
  Posted 3 months ago. Direct link to FreeRadical's post “The decay factor is the (...”
  The decay factor is the (1-r) part. Since r is a percent we subtract it from 1 to find how much is left after one round. For instance if you have 100 cookies and you eat 10% every minute, after 1 minute how many would you have?
  We take the number we have and multiply by 90% to find how much is left (1 - .1 = 0.9 which is 90%)
  100*(1-0.1)^1
  100*0.9 = 90 cookies
  So, unlike in growth functions where we ADD the rate to 1, in decay we SUBTRACT the rate from 1
  Button navigates to signup page
  (2 votes)
ryan.wheatley
Posted 2 months ago. Direct link to ryan.wheatley's post “can a growth factor be ne...”
can a growth factor be negative
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(2 votes)
Answer
- TheReal3A
  Posted a month ago. Direct link to TheReal3A's post “Good question! It turns o...”
  Good question! It turns out that the answer for that is no, not really...
  
  If the growth factor is negative, then for non-integer values of x, we would be raising a negative number to a fractional power, which does not result in a real number. For an exponential function with negative growth factor, the domain is limited to integer values of x.
  This issue does not occur when the growth factor is positive, since you can plug in any positive number raised to a fractional power.
  
  Here's an exercise: Plug in the values of (-2)^(0.5) and (2)^(0.5) into a regular calculator. Only the (-2)^(0.5) would result in a math error.
  
  Happy learning.
  Button navigates to signup page
  (2 votes)
Renu Sharma
Posted 6 months ago. Direct link to Renu Sharma's post “how do these relationship...”
how do these relationships even work? like I tried to find the constant closest In the linear vs exponential growth and when I did it was wrong and the number far away from the table numbers were right
how does that make sense.
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(2 votes)
Answer
Mrhylian
Posted 4 months ago. Direct link to Mrhylian's post “What type of mathematics ...”
What type of mathematics is used in aerospace engineering? I get this could be a broad question but I'm genuinely curious.
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(2 votes)
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Jackson Wagner
Posted 7 days ago. Direct link to Jackson Wagner's post “For certain problems that...”
For certain problems that are not continuous for example a bank account that applies interest monthly shouldn't problems like this technically be step functions because since it only increases on certain intervals any values in between those intervals wouldn't increase, like that bank account should only increase every month so all points on the graph in-between months should be the same right? of course I think this isn't relevant to all exponentials just mainly to ones that have explicit amount of times it's compounded by.
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(1 vote)
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Drake Rochelle, The Parallax Barrier Guy
Posted 8 months ago. Direct link to Drake Rochelle, The Parallax Barrier Guy's post “Why does everyone say the...”
Why does everyone say they don't understand this? It's very easy for me, so maybe I could help?
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(1 vote)
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rndcosta
Posted 3 months ago. Direct link to rndcosta's post “How do we determine if f(...”
How do we determine if f(x) is going to positive or negative infinity?
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(1 vote)
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Ibrahim Ahmed
Posted 5 months ago. Direct link to Ibrahim Ahmed's post “hello so i have 2 questio...”
hello so i have 2 questions:

1) isnt linear and exponential function same as arithmetic and geometric sequences?

2) can an exponential function say grow till it stops at f(x) = 50 for example? or an exponential decay that stops at f(x) = -50? or does every exponential function never stop?
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- joshua
  Posted 5 months ago. Direct link to joshua's post “1) Yes. They are the same...”
  1) Yes. They are the same. But when you are describing a sequence rather than a function in general, you will use arithmetic and geometric instead.
  
  2) Yes and no. It can tend to a value like 50, but never reaches it.
  
  For example f(x) = 2^x. It cannot reach 0, but you would say when x reaches negative infinity, f(x) = 0.
  Button navigates to signup page
  (2 votes)