2025 NASS P2 Q5

Secondary 4

9 marks

A scientist is studying how the concentration of a chemical solution (\(c\), in mg/L) decreases over time (\(t\), in hours) during a natural breakdown process.

The table below shows some recorded values of \(t\) and \(c\).

\(t\)	\(0.8\)	\(1.0\)	\(1.2\)	\(1.4\)	\(1.8\)
\(c\)	\(21.0\)	\(15.0\)	\(10.8\)	\(7.5\)	\(2.1\)

It is believed that \(c\) and \(t\) are related by the equation \(c=at+\dfrac bt\), where \(a\) and \(b\) are constants.

Express the given equation in a form suitable for drawing a straight line graph, and using suitable scales, draw the graph for the values given on a graph paper.[4]
Use your graph to estimate the value of each of the constants \(a\) and \(b\).[3]
The chemical is considered harmful to plants when its concentration exceeds 30 mg/L.
Use your graph to determine whether the chemical is safe for plants at time \(t=0.5\). Justify your answer.[2]

Solution:

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Answer:(a) \(ct=at^2+b\); (b) \(a\approx-5\), \(b\approx20\); (c) \(c\approx37.5\text{ mg/L}>30\text{ mg/L}\), not safe.

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