Variables P and T are known to be connected by the relationship P = Abᵀ, where A and b are constants. Values of P are found for certain values of time, T.

Mark scheme

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

1. [B2] lg P = lg A + T lg b oe nfww Must be seen and not from wrong working
2. [B1] for lg P = lg A + T lg b isw, nfww
3. [B1] and correct comparison with y = mx + c soi
4. [B2] A = 10⁶ oe isw and b = 10^(3/7) oe isw
5. [B2] for A = 10⁶ oe isw
6. [B1] correct method which could be used to find A e.g. lgA = 6 or 12 = (3/7)×14 + lg A
7. [B2] for b = 10^(3/7) oe isw
8. [B1] correct method which could be used to find b e.g. lgb = (12-6)/(14-0) oe or 12 = 14lgb+6
9. [M1] lg P₁ = 8 and lg P₂ = 9 soi
10. [M1] leading to T₁ = 4.6 to 4.8 or T₂ = 6.8 to 7.2
11. [M1] If graph not used then allow M1 for substitution of their A and their b in the exponential equation as far as 10⁸/theirA = (theirb)^T and 10⁹/theirA = (theirb)^T OR substitution of their A and their b or their lgA and their lg b in the log equation lg10⁸ = their lg A + T(their lgb) or better and lg10⁹ = their lg A + T(their lgb) or better
12. [A1] Difference of correct times: T₂-T₁ where T₂ = 6.8 to 7.2 T₁ = 4.6 to 4.8 Answer in range 2.2 to 2.4 nfww
13. [M2] M1 for lg10⁸ = 8 and lg10⁹ = 9 and Change in lg P / Change in T = 3/7
14. [A1] Answer in range 2.2 to 2.4 nfww