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## Algebra 1

### Unit 12: 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

CCSS.Math:

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

## 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.