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## Algebra 1

### Course: Algebra 1>Unit 12

Lesson 7: Exponential vs. linear models

# Linear vs. exponential growth: from data (example 2)

Sal constructs a function that models cooling water. To do that, he decides whether the function is linear or exponential.

## Want to join the conversation?

• Why is the common ratio raised to the 1/2 power the same as the square root of itself? • Hi!

I think this can best be shown with a proof. It's actually quite simple.

Let the common ratio be r, and let's let r^(1/2)=y.

So:
r^(1/2) = y
By squaring both sides, we get:
r = y^2
Now we take the square root of both sides:
sqrt(r) = y
And since we know that y = r^(1/2), we can therefore conclude:
r^(1/2) = sqrt(r)
• How would you define "model"? Thank you ! • @ Sal uses a fraction in the exponent to solve the problem. His answer does not match the solutions provided and how he does it makes no sense at this point. He completely skipped over how the fraction on the exponent is supposed to work and he's basically using topics that haven't been covered to solve a problem, without explaining why it works. How am I supposed to solve a problem with a tool I don't know how to use? • hi, why take the square root is the same thing as making its exponent 1/2? like he did at: • Why is the common ratio raised to the 1/2 power the same as the square root of itself? • Sorry I'm confused. Is the temperature decreasing by 80% or 20%. Intuitively, I feel it is reducing by 20%. Am I missing something? • Would there perhaps be a more intuitive way of thinking about why a common ration raise to the 1/2 power is the same as the square root of itself?
Kelvin L.’s answer is great but it would otherwise help remembering it better.   