Firstly, we find the gradient and y-intercept, to be able to substitute in the values once we have made the equation in linear law form, Y = mX+c

y-intercept = 0.7 (as question states straight line cuts vertical axis at 0.70)

gradient = y2-y1/x2-x1 = 0.7-0 / 0-(-0.233) = 3.00 (3sf)

Now, we will make the equation y = 2-px^q into linear form.

px^q = 2-y

Apply lg to both sides

lg(px^q) = lg(2-y)

expand lg(px^q), and bring the power q to the front

lg(p) + qlg(x) = lg(2-y)

Now, we have an equation in the form Y=mX+c

lg(2-y) = qlg(x) + lg(p)

where lg(2-y) is Y

q is m,

lg(x) is X

and lg(p) is c

Hence, we can find the value of q by subbing in the gradient, and the value of lg(p) by subbing in the y-intercept.

q = 3

lg(p) = 0.7

p = 10^0.7

p = 5.01 (3sf)

Hence, p = 5.01, q=3

Very clear and easy to understand. The steps are systematic and neat. Good explanations, detailed.

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The explanation is very clear, especially when explaining how to get the linear form and which terms in the equation represent the Y, X, m and c.

ReplyDeleteThe explanation is very clear, as it clearly and methodically explains how he gets to the linear form and which terms in the equation represent the Y, X, m and c.

ReplyDeleteThe explanation is very clear, as it clearly and methodically explains how he gets to the linear form and which terms in the equation represent the Y, X, m and c.

ReplyDeleteThe explanation of the workings is very clear and easy to understand.

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