A 5000-gal aquarium is maintained with a pumping system that passes 100 gal of water per minute through the tank. To treat a certain fish malady, a soluble an- tibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te^−(t/50) mg/gal, where t is measured in minutes. The well-stirred mixture flows out of the aquarium at the same rate. (a) Solve for the amount of medicine in the tank as a function of time. (b) What is the maximum concentration of medicine achieved by this dosing and when does it occur? (c) For the antibiotic to be effective, its concentration must exceed 100 mg/gal for a minimum of 60 min. Was the dosing effective?

Assume the rate at which the zombies spread is jointly proportional to the number of encounters between the infected and the people who are not infected yet. At the time, there are 300 students, faculty and staff on campus. When the government hears about the accident, they barricade the entire campus so no one can escape. After four hours, 20 people are infected. How many will be infected after ten hours if the T-virus started with a zombie?

A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 25 meter tall building. You have a rope that has a mass of 0.3 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 15 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building. Joules

Tank B, a 30-litre tank, initially contains 6 grams of salt in 15 litres of water. At t = 0, saltwater with a concentration of 1 gram of salt per litre is poured from Tank A into Tank B at a rate of 2 litres per minute, while the well mixed solution leaves the bottom of Tank B at a rate of one litre per minute. a) derive the IVP that models the rate of change of the quantity of salt in Tank B with respect to time,b) solve the IVP, andc) determine the quantity and concentration of salt in Tank B at the instant Tank B is full