A fish population in a closed lake satisfies

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

\dfrac{dP}{dt}=200-0.05P

, where

P(t)

is the number of fish after

t

weeks. Which statement best describes the long-term behavior of

P(t)

? (a)

P(t)

increases without bound because the net rate is always positive. (b)

P(t)

approaches 5{,}000 and remains near that value. (c)

P(t)

approaches 4{,}000 and remains near that value. (d)

P(t)

oscillates indefinitely around 4{,}000 without settling.