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 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 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 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 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?

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 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?

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 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?

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)?