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Answers without the blur. Sign up and see all textbooks for free! Q. 45

Expert-verified Found in: Page 791 ### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339 # Suppose that the relationship between a response variable y and an explanatory variable x is modelled by $y=2.7{\left(0.316\right)}^{x}$. Which of the following scatterplots would approximately follow a straight line? (a) A plot of y against x (b) A plot of y against log x (c) A plot of log y against x (d) A plot of log y against log x (e) None of (a) through (d)

The scatterplots that approximately follow a straight line is option (c) A plot of log y against x.

See the step by step solution

## Step 1: Given information

The relationship between a response variable y and an explanatory variable x is modelled by $y=2.7{\left(0.316\right)}^{x}$.

## Step 2: Explanation

The given equation is

$y=2.7{\left(0.316\right)}^{x}$

The scatterplot will not be a straight line since this equation represents an exponential function, which is not linear.

If we multiply both sides of the equation by the logarithm, we get:

$\mathrm{log}y=\mathrm{log}\left[2.7\left(0.316{\right)}^{x}\right]=\mathrm{log}2.7+\mathrm{log}0.{316}^{x}=\mathrm{log}2.7+x\mathrm{log}0.316$

This is a linear equation with variables log $y$ and $x$ and thus the scatterplot will be a straight line in this case.

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