2026 PHS P2 Q3

Secondary 4

9 marks

A manufacturing firm purchases a laser-cutting machine.
The value of the machine, $V$ (in thousands of dollars), after $t$ years is modelled by
$V=500\times(0.8)^t$.
Find the initial value of the laser-cutting machine.[1]
On the grid below, draw the graph of $V=500\times(0.8)^t$ for $2\le t\le10$.[3]
$t$ $2$ $4$ $6$ $8$ $10$
$V$ $320$ $205$ $131$ $83.9$ $53.7$
By drawing a tangent, work out an estimate for the gradient of the graph when $t=5$.[2]
Given that another graph of $y=90\times a^{-x}$ where $a>0$, passes through $\left(3,\dfrac{45}4\right)$, find the value of $a$.[3]

\(t\)	\(2\)	\(4\)	\(6\)	\(8\)	\(10\)
\(V\)	\(320\)	\(205\)	\(131\)	\(83.9\)	\(53.7\)

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Answer:(a) $500 000 (b) See graph. (c) Approximately $-36.6$ (graphical estimate) (d) $a=2$

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