The variables x and y satisfy the equation y = A × Blnx, where A and B are constants. The graph of In y against Inx is a straight line passing through the points (2.2, 4.908) and (5.9, 11.008), as shown in the diagram. Find the values of A and B correct to 2 significant figures. [Figure 2]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B1] State or imply equation ln y = ln A + ln B ln x
2. [M1] Equate gradient of line to ln B
3. [A1] Obtain ln B = 1.6486... and hence B = 5.2
4. [M1] Substitute appropriate values to find ln A
5. [A1] Obtain ln A = 1.2809... and hence A = 3.6
6. Or
7. [B1] State or imply equation ln y = ln A + ln B ln x
8. [B1] Use given coordinates to obtain a correct equation
9. [M1] Use given coordinates to obtain a second correct equation and attempt to solve both equations simultaneously to obtain at least one of the unknowns ln A or ln B
10. [A1] Obtain ln B = 1.6486... and hence B = 5.2
11. [A1] Obtain ln A = 1.2809... and hence A = 3.6
12. Or
13. [B1] Use given coordinates to obtain a correct equation
14. [B1] Use given coordinates to obtain a second correct equation
15. [M1] Solve to obtain B
16. [A1] B = 5.2
17. [A1] A = 3.6