EXM.1.AHL.TZ0.13

pestleMathematicsAIHLPaper 1EXM· ahl-2-10-scaling-large-numbers-log-log-graphssource ↗

It is believed that two variables, $m$ and $p$ are related. Experimental values of $m$ and $p$ are obtained. A graph of ${\text{ln}}\,m$ against $p$ shows a straight line passing through (2.1, 7.3) and (5.6, 2.4).

Hence, find

Find the equation of the straight line, giving your answer in the form ${\text{ln}}\,m = ap + b$ , where $a{\text{,}}\,\,b \in \mathbb{R}$ .

[3]

a formula for $m$ in terms of $p$ .

[1]

b.i.

the value of $m$ when $p = 0$ .

[1]

b.ii.

Markscheme / solution

gradient = −1.4 A1

${\text{ln}}\,m - 7.3 = - 1.4\left( {p - 2.1} \right)$ M1

${\text{ln}}\,m = - 1.4p + 10.24$ A1

[3 marks]

$m = {e^{ - 1.4p + 10.24}}\,\,\left( { = 28000{e^{ - 1.4p}}} \right)$ A1

[1 mark]

b.i.

28000 A1

[1 mark]

b.ii.

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.