An experiment was carried out and values of y for certain values of x were recorded. The table shows the values recorded. x 15 30 45 60 75 y 10 13 22 35 50 The relationship between y and x is modelled by y = Ae^(kx), where A and k are constants.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B2] Points plotted at x 15 30 45 60 75 lny 2.3 2.5 3.1 3.5 3.9 or or 2.6 3.6
2. [B2] B1 for at least 4 correctly plotted points
3. [B2] soi
4. [B2] and single, ruled, straight line of best fit drawn
5. [M1] lny = 0.03x + 1.8
6. [M1] for m = awrt 0.02 to awrt 0.03
7. [M1] or c = awrt 1.7 to awrt 2.0
8. [M1] or for the straight line form in terms of lnA and k: lny = lnA + kx[lne]
9. [B3] A = 6 or A = 7
10. [B3] Must have been found using linear points or linear equation
11. [B3] B2 for A = 6 or A = 7
12. [B3] or A in range: awrt 6 or awrt 7
13. [B3] or B1 FT for lnA = their 1.8 or A = e^(their1.8)
14. [B3] and k = 0.03 or k = 0.02
15. [B3] B1 FT for k = 0.03 or 0.02 or k in range: awrt 0.02 or awrt 0.03
16. [B3] Maximum of 2 marks if one or both values not rounded to 1 sf
17. [B3] If B0 scored, award SC1 for A = 6 or A = 7 and SC1 for k = 0.03 or k = 0.02 found not using transformed data
18. [M1] A value of x in range 33 ≤ x ≤ 37.5 nfww, isw
19. [M1] for lny = 2.8 or 2.83[32...]
20. [M1] OR A value of x in range 29.5 < x <33 or 37.5 ≤ x < 45 nfww
21. [M1] OR STRICT FT for x = (ln17 - their lnA) / their k
22. [M1] OR STRICT FT for x = (1/their k) * ln(17/their A)