21M.1.SL.TZ2.1

pestleMathematicsAISLPaper 121M· sl-2-5-modelling-functionssource ↗

The amount, in milligrams, of a medicinal drug in the body $t$ hours after it was injected is given by $D (t) = 23 (0.85)^{t}, t \geq 0$ . Before this injection, the amount of the drug in the body was zero.

Write down

the initial dose of the drug.

[1]

a.i.

the percentage of the drug that leaves the body each hour.

[2]

a.ii.

Calculate the amount of the drug remaining in the body $10$ hours after the injection.

[2]

Markscheme / solution

$23 mg$ A1

[1 mark]

a.i.

$1 - 0.85$ OR $\frac{23 - 19.55}{23}$ OR $0.15$ (M1)

$15 (%)$ A1

[2 marks]

a.ii.

$23 {(0.85)}^{10}$ (M1)

$4.53 mg (4.52811 \dots)$ A1

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]