Question: Oil reserves decrease at a constant proportional rate, k > 0, so that dN/dt = -kN where N denotes the number of barrels of oil

Oil reserves decrease at a constant proportional rate, k > 0, so that
dN/dt = -kN
where N denotes the number of barrels of oil remaining in t years’ time.
(a) Write down an expression for N(t) when current oil reserves are A barrels.
(b) Show that the time taken for oil reserves to fall to half their current levels is (ln 2)/k.

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