A mixing tank initially holds 100 L of brine containing 30 kg of salt

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A mixing tank initially holds 100 L of brine containing 30 kg of salt. Brine with a concentration of 0.40 kg/L flows in at 3 L/min, while the well-mixed solution is pumped out at 5 L/min. Let S(t)S(t) denote the amount of salt (in kg) in the tank after tt minutes, while the tank still contains liquid. Which differential equation correctly models S(t)S(t)? (a) dSdt=1.2−5S100\displaystyle \frac{dS}{dt}=1.2-\frac{5S}{100} (b) dSdt=1.2−3S100−2t\displaystyle \frac{dS}{dt}=1.2-\frac{3S}{100-2t} (c) dSdt=1.2−5S100−2t\displaystyle \frac{dS}{dt}=1.2-\frac{5S}{100-2t} (d) dSdt=5S100−2t−1.2\displaystyle \frac{dS}{dt}=\frac{5S}{100-2t}-1.2

Related theory

Browse the problem library