Find the value of $K$.

In the context of the model, state what the horizontal asymptote represents.

Find Jean-Pierre’s vertical speed after $10$ seconds. Give your answer in $\text{km} {\text{h}}^{-1}$ .

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

$0=K-60\left(1.2^0\right)$      (M1)

Note: Award (M1) for correctly substituted function equated to zero.

$\left(K=\right) 60$      (A1)    (C2)

[2 marks]

the (vertical) speed that Jean-Pierre is approaching (as $t$ increases)     (A1)    (C1)
OR
the limit of the (vertical) speed of Jean-Pierre     (A1)    (C1)

Note: Accept “maximum speed” or “terminal speed”.

[1 mark]

$\left(S=\right) 60-60\left(1.2^{-10}\right)$     (M1)

Note: Award (M1) for correctly substituted function.

$\left(S=\right) 50.3096\dots \left({\text{m\hspace{0.05em}s}}^{-1}\right)$     (A1)(ft)

Note: Follow through from part (a).

$181 \left({\text{km\hspace{0.05em}h}}^{-1}\right) \left(181.114\dots \left({\text{km\hspace{0.05em}h}}^{-1}\right)\right)$     (A1)(ft)       (C3)

Note: Award the final (A1)(ft) for correct conversion of their speed to $\text{km} {\text{h}}^{-1}$.

[3 marks]