How do we determine if a function is exponential?

A function is exponential if the common ratio is raised to the variable power The example from the video is g(t) = -2 * 1/7^t

Exponential functions looks a lot like geometric sequences, is it related in some way?

Yes. When values of a function have a common ratio its called a geometric function.

i use the formula y=ab^x is this ok?

Yes, so long as you follow the same steps as shown in the video your formula is fine! In this video, Sal used r instead of b because of the r in common ratio :)

what are the exponential functions and how many are thier

There have to be an infinite number due to the fact that both the initial value and the base could be an infinite amount of numbers.

How do we determine if a function is exponential?

A function is exponential if it has a common ratio instead of common difference.

Find an equation in the form y=ab^x of the exponential curve that contains the points (0,3.5) and (7,57344) How to calculate step by step ?

So the y intercept gives you a = 3.5. Putting this in the formula, you have y=3.5 b^x. Substitute the point in, 57344=3.5 b^7 and solve for b by dividing by 3.5 and then taking the 7th root.

Main content

Algebra I (2018 edition)

Course: Algebra I (2018 edition) > Unit 13

Lesson 6: Exponential functions from tables & graphs

Writing exponential functions

Name: Writing exponential functions
Uploaded: 2016-04-13T11:16:05Z
Description: Writing the exponential function whose initial value is -2 and common ratio is 1/7.

Google Classroom

Writing the exponential function whose initial value is -2 and common ratio is 1/7.

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Bob The Zealot
Posted 8 years ago. Direct link to Bob The Zealot's post “How do we determine if a ...”
How do we determine if a function is exponential?
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(20 votes)
Answer
- Nemo
  Posted 8 years ago. Direct link to Nemo's post “A function is exponential...”
  A function is exponential if the common ratio is raised to the variable power
  The example from the video is g(t) = -2 * 1/7^t
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  (13 votes)
Xyla Ardhia F.
Posted 7 years ago. Direct link to Xyla Ardhia F.'s post “Exponential functions loo...”
Exponential functions looks a lot like geometric sequences, is it related in some way?
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(5 votes)
Answer
- Ray
  Posted 7 years ago. Direct link to Ray's post “Yes. When values of a fun...”
  Yes. When values of a function have a common ratio its called a geometric function.
  Comment on Ray's post “Yes. When values of a fun...”
  (6 votes)
jpejzeke
Posted 5 years ago. Direct link to jpejzeke's post “what are the exponential ...”
what are the exponential functions and how many are thier
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(1 vote)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “There have to be an infin...”
  There have to be an infinite number due to the fact that both the initial value and the base could be an infinite amount of numbers.
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  (9 votes)
David Campagna
Posted 5 years ago. Direct link to David Campagna's post “i use the formula y=ab^x ...”
i use the formula y=ab^x is this ok?
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(2 votes)
Answer
- Iris Nogueroles Langa
  Posted 5 years ago. Direct link to Iris Nogueroles Langa's post “Yes, so long as you follo...”
  Yes, so long as you follow the same steps as shown in the video your formula is fine!
  
  In this video, Sal used r instead of b because of the r in common ratio :)
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  (5 votes)
Ali
Posted 5 years ago. Direct link to Ali's post “In sequences, the formula...”
In sequences, the formula is
initial x cr^t-1
. Why is this
initial x cr^t
? How do you determine when to use t-1 and when to use t?
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(3 votes)
Answer
- Sir.Isaac.Newton.06
  Posted 3 years ago. Direct link to Sir.Isaac.Newton.06's post “It depends on whether you...”
  It depends on whether your starting value is considered "term 0" or "term 1." Technology, on a graph it should always be zero, but sometimes we refer to the start as #1. sorry this is three years late
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  (1 vote)
Garcia, Diego
Posted 3 years ago. Direct link to Garcia, Diego's post “How do we determine if a ...”
How do we determine if a function is exponential?
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(1 vote)
Answer
- Mango
  Posted 6 months ago. Direct link to Mango's post “A function is exponential...”
  A function is exponential if it has a common ratio instead of common difference.
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  (3 votes)
Lucio
Posted 7 years ago. Direct link to Lucio's post “why is "times" the only o...”
why is "times" the only operator that can be there? why can't it be -2 OVER (1/7)^t?
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(3 votes)
Answer
Guantum Realm
Posted 3 years ago. Direct link to Guantum Realm's post “Shouldn't Sal have put pa...”
Shouldn't Sal have put parentheses around the 1/7?
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(2 votes)
Answer
- Shane Sarosh
  Posted 3 years ago. Direct link to Shane Sarosh's post “It isn't necessary becaus...”
  It isn't necessary because it doesn't affect the order of operations in any way. Exponentiation first, and then multiplication.
  Comment on Shane Sarosh's post “It isn't necessary becaus...”
  (1 vote)
Ethan Tran
Posted 7 years ago. Direct link to Ethan Tran's post “In the formula f(x) = a*r...”
In the formula f(x) = a*r^x +d, a is the initial value, r is the common ratio and d is the one time increase. What is a one time increase and how would we calculate it?

Example: h(x) = 4^x + 1. Write h(x) in the form f(x) = a*r^x +d.
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(1 vote)
Answer
Forla Huang
Posted 2 years ago. Direct link to Forla Huang's post “Find an equation in the f...”
Find an equation in the form y=ab^x of the exponential curve that contains the points (0,3.5) and (7,57344)

How to calculate step by step ?
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(1 vote)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “So the y intercept gives ...”
  So the y intercept gives you a = 3.5.
  Putting this in the formula, you have y=3.5 b^x. Substitute the point in, 57344=3.5 b^7 and solve for b by dividing by 3.5 and then taking the 7th root.
  Button navigates to signup page
  (2 votes)

Video transcript

- [Voiceover] g is an exponential function with an initial value of -2. So, an initial value of -2, and a common ratio of 1/7, common ratio of 1/7. Write the formula for g(t). Well, the fact that it's an exponential function, we know that its formula is going to be of the form g(t) is equal to our initial value which we could call A, times our common ratio which we could call r, to the t power. It's going to have that form. And they tell us what the initial value is. It's -2. So this right over here is -2. And we know that the common ratio is 1/7. So this is 1/7. So let me just write it again a little bit neater. g(t) is going to be equal to our initial value, -2, times times our common ratio, 1/7, to the t power. And hopefully this makes sense. Initial value is this number. Well, if t is equal to 0, then 1/7 to the zero power is 1. And so g(0), you could do that at time as being equal to zero if your t is time, would be equal to -2. So that would be our initial value. And then if you think about it, every time you increase t by one, you're going to mulitply by 1/7 again. And so, the ratio between successive terms is going to be 1/7. And so that's why we call that the common ratio. Hopefully, you found that interesting.