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## Operations and Algebraic Thinking 229+

### Course: Operations and Algebraic Thinking 229+ > Unit 8

Lesson 6: Exponential functions from tables & graphs- Writing exponential functions
- Writing exponential functions from tables
- Exponential functions from tables & graphs
- Writing exponential functions from graphs
- Analyzing tables of exponential functions
- Analyzing graphs of exponential functions
- Analyzing graphs of exponential functions: negative initial value
- Modeling with basic exponential functions word problem
- Connecting exponential graphs with contexts

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# Writing exponential functions

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

## Want to join the conversation?

- How do we determine if a function is exponential?(20 votes)
- 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(13 votes)

- Exponential functions looks a lot like geometric sequences, is it related in some way?(5 votes)
- Yes. When values of a function have a common ratio its called a geometric function.(6 votes)

- what are the exponential functions and how many are thier(1 vote)
- 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.(9 votes)

- i use the formula y=ab^x is this ok?(2 votes)
- 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 :)(5 votes)

- In sequences, the formula is

. Why is this`initial x cr^t-1`

? How do you determine when to use t-1 and when to use t?`initial x cr^t`

(3 votes)- 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(1 vote)

- How do we determine if a function is exponential?(1 vote)
- A function is exponential if it has a common ratio instead of common difference.(3 votes)

- why is "times" the only operator that can be there? why can't it be -2 OVER (1/7)^t?(3 votes)
- Shouldn't Sal have put parentheses around the
`1/7`

?(2 votes)- It isn't necessary because it doesn't affect the order of operations in any way. Exponentiation first, and then multiplication.(1 vote)

- 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.(1 vote) - 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 ?(1 vote)- 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.(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.