The variables x and y are related by the equation y = ab^x, where a and b are constants. The diagram shows the result of plotting In y against x for two pairs of values of x and y. The coordinates of these points are (1, 3.7) and (2.2, 6.46). [Figure 3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [B1] State or imply that ln y = ln a + x ln b
2. [M1] Carry out a completely correct method for finding ln a or ln b 3.7=ln a+ln b and 6.46=ln a +2.2 ln b leading to ln a=1.4, ln b=2.3.
3. [A1] Obtain value a = 4.06
4. [A1] Obtain value b = 9.97
5. [B1] Alternative Method: e^3.7 = ab¹ and e^6.46 = ab^2.2
6. [M1] Alternative Method: Divide to obtain e^2.76 = b^1.2 and state or imply 2.76=1.2lnb
7. [A1] Alternative Method: Obtain value a = 4.06
8. [A1] Alternative Method: Obtain value b = 9.97