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## Algebra I (2018 edition)

### Course: Algebra I (2018 edition)>Unit 13

Lesson 1: Exponential vs. linear growth

# Exponential vs. linear models: table

Determining whether real world model is linear or exponential, where the model is given as a table.

## Want to join the conversation?

• Is there a quicker method to find whether something is exponential or linear, or is this the quickest way?
• On a graph, an exponential function is always curved (like a gradual slope) and a linear function is always straight (like a line). Hope that helps! :)
• What if the x-values increase at random? A sequence like 1, 5, 6, 9, 10, 17 et cetera.
• You just need to find the slope using two points. You just need to find the slope between x=1 and x=5, x=5 and x=6, x=6, x=9, etc. If the slopes are the same, it's linear and if they're different, it's exponential.
Hope this helps! If you have any questions or need help, please ask! :)
• Are there any quicker ways
• Given only a table of numbers, there is not a quicker way. If you have a graph, it is easy to see that exponential graphs have a curve whereas linear graphs are completely straight.
• At about minutes into the video, Sal said; "It seems like we're multiplying by a slightly lower factor".
What does he mean by this?
How can he tell by just looking at the table, that it's a slightly lower factor?
• He is explaining why it isn't an exponential function by showing that the factors between each number isn't constant.

He didn't just find it by looking at the table, he probably used a calculator off-screen while not recording this video.
• By approximating the cost differences to 7 (in thousands of dollars), is the function mathematically a linear function?
• I don't know if I'm right, but here's just my thoughts:
If when you're plotting the points on the graph and you just increase by 7 (you've already rounded it), then yes, the function will be linear.
If you plot the points precisely on the graph, it would look very much like a linear function, except the slope between each points would vary by a little bit. But to me, I'd just say it's a linear. But I think you can also call it a piecewise graph.
• How do you valuate when an exponential function and a linear function are equal?
I have only seen examples with tables, but isn't there a way to equal the two functions and isolate the variable?
• Yes if you look at the chart and try to find the starting number
• Can an exponential function be dividing?
• Isnt there a quicker method or formula for this problem?