The variables x and y are such that when lny is plotted against x, a straight line graph is obtained. This line passes through the points x = 4, lny = 0.20 and x = 12, lny = 0.08.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

1. [1] (i) ln y = ln A + x ln b B1 may be implied, if equation not seen specifically, by correct values for A and b
2. [1] (i) Gradient: ln b = (0.08 - 0.20) / (12 - 4) = -0.12 / 8 = -0.015 M1 for use of gradient to obtain ln b
3. [1] (i) b = 0.985 A1 Allow A1 for e⁻⁰·⁰¹⁵
4. [1] (i) Intercept: ln A = 0.26 DM1 for use of one of the given points correctly
5. [1] (i) A = 1.30 A1 Allow A1 for e⁰·²⁶ or 1.3
6. [1] (ii) When x = 6, ln y = ln A + 6 ln b M1 for ln y = their ln A + 6 their ln b or y = their A × (their b)⁶
7. [1] (ii) y = 1.19 A1 allow awrt 1.18 to 1.20
8. [1] (iii) When y=1.1, ln y = 0.095 M1 for ln 1.1 = their ln A + x their ln b or 1.1 = their A × (their b)ˣ
9. [1] (iii) x = 11 A1 allow 10.5 to 11.5