2024 FMSS PRELIMS P1 Q9
2024 FMSS PRELIMS P1 Q9
9 marks
- The variables \(x\) and \(y\) increase in such a way that when \(x = 3\), the rate of increase of \(y\) with respect to time is three times the rate of increase of \(x\) with respect to time. Given that \(y = k\sqrt{3x + 7}\), where \(k\) is a constant, find the value of \(k\).[4]
- The mass, \(m\) grams, of a radioactive sample, present at time \(t\) days after being observed, is given by \(m = 24\mathrm{e}^{-0.02t}\).Find
- the initial mass of the radioactive sample,[1]
- the time taken for the sample to decrease to half its initial mass,[2]
- the rate at which the mass is decreasing after \(12\) hours.[2]
Solution:
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Answer:(a) \(k=8\) (b)(i) \(24\text{ g}\) (ii) \(50\ln2\text{ days}\approx34.7\text{ days}\) (iii) Decreasing at \(0.475\text{ g/day}\).
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