An experiment was carried out recording values of y for certain values of x. The variables x and y are thought to be connected by the relationship y = axⁿ, where a and n are constants. The values of ln y and ln x were plotted and a line of best fit drawn. This is shown in the diagram below. [Figure 8.1]

Mark scheme

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

1. [1] (i) Takes logs of both sides
2. [1] (i) ln y = ln a + n ln x or lg y = lg a + n lg x
3. [1] (ii) n = -0.2 to -0.3 nfww
4. [1] (ii) attempts to equate y-intercept to ln a or forms their ln equation with their gradient and a point on the line or uses two points on the line to form a pair of simultaneous equations
5. [1] (ii) a = e^4.7 isw or 110 or 109.9[47...]
6. [1] (ii) maximum of 2 marks if no coordinates stated
7. [1] (iii) use of ln(50) and lnx = 3 to 3.2
8. [1] (iii) or for 50/(theira) = x^(their n) or better or for ln 50 = ln(theira) + (their n) lnx oe
9. [1] (iii) awrt 22 or 23 to 2 significant figures