A tank initially contains 1000 liters of saltwater with a salt concentration of 2 g/L. Freshwater is poured into the tank at a rate of 5 L/min, and the well-stirred mixture is drained from the tank at the same rate. The rate of change of salt in the tank can be modeled by which differential equation?

A drug is administered to a patient at a rate of 2 mg/min. The drug concentration in the patient's bloodstream decreases at a rate proportional to the current concentration. If the concentration is 8 mg/L at t = 0, what is the concentration after 20 minutes?

A car's speed is modeled by the differential equation dv/dt = 3t, with an initial speed of 10 m/s. What is the speed after 5 seconds (t = 5)?

A particle is moving with a velocity of v(t) = 2t - 3 m/s. What is the displacement of the particle from its starting position after 5 seconds?

The rate of change of a chemical reaction's concentration is proportional to its current concentration. If the concentration is 0.1 mol/L at t = 0, and it doubles after 5 minutes, what is the reaction rate constant (k) per minute?

A car's speed is decreasing at a rate of 5 m/s². If its initial speed was 30 m/s, what is its speed after 8 seconds?

A sample of a radioactive substance initially contains 1000 atoms, and it decays at a rate of 5% per minute. How many atoms remain after 10 minutes?

A population of rabbits is growing at a rate proportional to the current population. If the population doubles in 2 years, what is the population growth rate as a percentage per year?

A bank account has an initial balance of $1000, and it accrues interest continuously at a rate of 4% per year. Which differential equation represents the rate of change of the account balance over time?

A water tank initially contains 500 liters of water. Water is drained from the tank at a rate of 10 L/min, and fresh water is poured into the tank at a rate of 5 L/min. Which differential equation describes the change in the volume of water in the tank over time?