2026 GESS P2 Q11

2026 GESS P2 Q11

Secondary 4
10 marks

Recorded values of the population \(P\), in millions, of a bacteria colony, \(x\) minutes after observations began, are shown in the table below.

\(x\)\(5\)\(10\)\(15\)\(20\)\(25\)
\(P\)\(35.6\)\(68.2\)\(75.1\)\(145.7\)\(188.6\)

It is known that \(P=ax^n+12\), where \(a\) and \(n\) are constants. It is believed that an error was made in recording one of the values of \(P\).

  1. Plot \(\lg(P-12)\) against \(\lg x\) and draw a straight line graph on the grid below to illustrate the information.[3]

Use the graph to estimate

  1. a value of \(P\) to replace the incorrect reading,[2]
  2. the value of each of the constants \(a\) and \(n\).[5]

Solution:

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Answer:(a) See graph; anomalous point at \(x=15\). (b) About 105 million from the drawn line (graphical tolerance applies). (c) \(n\approx1.25,a\approx3.16\).

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