The variables x and y satisfy the equation y = Ax^(-2p), where A and p are constants. The graph of ln y against ln x is a straight line passing through the points (-0.68, 3.02) and (1.07, -1.53), as shown in the diagram. [Figure 4.1] Find the values of A and p.

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

1. [B1] State or imply equation is ln y = ln A - 2p ln x
2. [M1] Equate gradient of line to -2p
3. [A1] Obtain -2p = -2.6 and hence p = 1.3
4. [M1] Substitute appropriate values to find ln A
5. [A1] Obtain ln A = 1.252 and hence A = 3.5
6. Alternative method for question 4
7. [B1] State or imply equation is ln y = ln A - 2p ln x
8. [M1] Substitute given coordinates to obtain 2 simultaneous equations and solve to obtain 3.5p
9. [A1] Obtain 3.5p = 4.55 and hence p = 1.3
10. [M1] Substitute appropriate values to find ln A
11. [A1] Obtain ln A = 1.252 and hence A = 3.5