A fish population in a closed lake satisfies dtdP=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.