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