### Video Transcript

Which of the following scatter plots shows π relationship that is appropriately modelled by the equation π¦ equals π multiplied by π₯ to the power of π, where π is positive and π is negative.

Options A and D show a negative correlation, even though option D is a relatively weak negative correlation. In both of these cases, as the value of π₯ increases, the value of π¦ decreases. Option B has no correlation. This means that there is no length between the variable π₯ and the variable π¦. We can therefore say that there is no equation that models the relationship in scatter plot B. Option C demonstrates a positive correlation between π₯ and π¦. As the value of π₯ increases, so does the value of π¦. If we were to draw a line of best fit on option D, we would have a straight line. This means that option D shows a linear relationship.

The equation that models this would be of the type π¦ equals ππ₯ plus π, where π is the slope or gradient and π is the π¦-intercept. This is not of the form π¦ equals π multiplied by π₯ to the power of π. We have, therefore, ruled out options B and D. Both options A and C demonstrate an exponential relationship. The lines of best fit are shown on the scatter plots. And the equations would be of the form π¦ equals π multiplied by π₯ to the power of π. Option A represents exponential decay. As already mentioned, as the value of π₯ increases, the value of π¦ decreases.

Option C, on the other hand, represents exponential growth. As the value of π₯ increases, π¦ also increases. When dealing with exponential decay, our value of π, the power or exponent, is negative. Whereas with exponential growth, it is positive. Weβre told in this question that π is negative. This rules out option C. We can, therefore, conclude that the correct answer is option A. This is the scatter plot that shows a relationship that is modelled by the equation π¦ equals π multiplied by π₯ to the π, where π is positive and π is negative.