Question

Suppose that the relationship between a response variable y and an explanatory variable x is modelled by $y=2.7{(0.316)}^x$. Which of these 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. A plot of$y^{\sqrt{y}}$ against x

Short answer

The scatterplots that approximately follow a straight line is option (c).

Step-by-step solution

Given information

The variable $x$is modelled by$y=2.7{(0.316)}^x$

Explanation

The given data is

$y=2.7{(0.316)}^x$

Because this equation depicts a nonlinear exponential function, the scatter plot will be a straight line.

If both sides of the equation are logarithmized, the equation is a linear equation with variables $\log y$and $x$, and the scatter plot would be a straight line in this case.

As a result, the best solution is (c).