The fish population in a closed pond satisfies the differential equation
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
The fish population P(t) in a closed pond satisfies the differential equation dtdP=−0.3(P−800), where t is measured in months.
Which statement is most consistent with this model?
(a) The population approaches 0 fish over time because the coefficient −0.3 indicates exponential decay.
(b) The population approaches 800 fish over time because it decreases when above 800 and increases when below 800.
(c) The population oscillates about 800 fish because the sign of the derivative alternates periodically.
(d) The population decreases linearly toward 800 fish because the rate of change is the constant −0.3.