2025 AHS PRELIMS P1 Q14
2025 AHS PRELIMS P1 Q14
Secondary 4
10 marks
The mass, \(m\) grams, of the decomposition of a radio-active substance is given by the formula
\[m=ae^{-bt}\]
where \(a\) and \(b\) are constants, and \(t\) is the number of weeks after the initial measurement of the mass. Experimental values of \(t\) and \(m\) are given in the table below.
| \(t\) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \(m\) | 1.51 | 0.454 | 0.137 | 0.0183 | 0.0124 |
- What does the constant \(a\) refer to?[1]
- By drawing a suitable straight line graph using the data provided, estimate the value of \(a\) and of \(b\).[7]
- It is discovered that one of the readings of the mass, \(m\), is incorrect. Using your graph, estimate the correct value for this incorrect reading.[2]
Solution:
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Answer:(i) \(a\) is the initial mass of the radio-active substance, in grams. (ii) \(a\approx5.00\) and \(b\approx1.20\text{ weeks}^{-1}\). (iii) The corrected reading is \(m\approx0.0412\text{ g}\) when \(t=4\).
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