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June 2018 p31 q6
2289
In a certain chemical reaction the amount, x grams, of a substance is decreasing. The differential equation relating x and t, the time in seconds since the reaction started, is
\(\frac{dx}{dt} = -\frac{kx}{\sqrt{t}}\),
\(where k is a positive constant. It is given that x = 100 at the start of the reaction.\)
- Solve the differential equation, obtaining a relation between x, t and k.
- Given that t = 25 when x = 80, find the value of t when x = 40.
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