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Nov 2022 p31 q8
2286
In a certain chemical reaction the amount, x grams, of a substance is increasing. The differential equation satisfied by x and t, the time in seconds since the reaction began, is
\(\frac{dx}{dt} = kxe^{-0.1t}\),
\(where k is a positive constant. It is given that x = 20 at the start of the reaction.\)
(a) Solve the differential equation, obtaining a relation between x, t and k.
(b) Given that x = 40 when t = 10, find the value of k and find the value approached by x as t becomes large.
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