1. A tank starts with 100 litres of water and 1,000 bacteria in it. For now...

1. A tank starts with 100 litres of water and 1,000 bacteria in it. For now we assume the bacteria do not reproduce. Let B(t) be the number of bacteria in the tank as a function of time, where t is in hours. For each of the situations below, write down a first order differential equation satisfied by B(t), of the form dB dt = f(t, B). You DO NOT need to solve it.

(a) A little goblin is pouring bacteria into the tank at a rate of 2020 bacteria per hour.

(b) Like part (a), but we are also draining the tank at a rate of 3 litres per hour.

(c) Like part (b), but now the bacteria are reproducing. Suppose that the bacteria will double the present population in every hour. A gentle reminder: make sure that you write down the meaning of each term.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

A rigid tank with a volume of 20 litres initially contains water at 0.1 degree of...

A rigid tank with a volume of 20 litres initially contains water at 0.1 degree of dryness and a pressure of 175 KPA. A steam disposal Valve is located at the top of the tank. Adding heat and steam by throwing the final case degree of dryness 0.4 and pressure 150 kPa is desired to be made. How much mass is ejected and what is the entropy produced. Heat source temperature 1000 K.

A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...

A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 4 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at...

A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...

A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 6 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at...

A tank contains 100 gal of water. Brine enters the tank at the rate of 3...

A tank contains 100 gal of water. Brine enters the tank at the rate of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at the rate of 2 gal/min. If the salt concentration in the brine at the end of 20 minutes is to be 2 lb/gal, what should be the salt concentration in the brine entering the tank?

A tank contains 100 gal of water. Brine enters the tank at the rate of 3...

Let m > 0 be a constant. Suppose a tank starts with 10kg of salt water...

Let m > 0 be a constant. Suppose a tank starts with 10kg of salt water with 1% salt by mass. Suppose further that every hour, m kg of salt water with a concentration of 10% salt is added, and 2kg of the water in the tank is drained. The solution is kept well mixed at all times. (a) (2 points) Write a diﬀerential equation that describes the amount of salt in the water. (b) (5 points) How long does...

A holding tank with capacity 5000 litres initially contains 1500 litres of 25 mM NaCl solution....

A holding tank with capacity 5000 litres initially contains 1500 litres of 25 mM NaCl solution. a) What is the final concentration of NaCl (expressed in mM) if an additional 3000 litres of 25 mM NaCl solution is pumped into the tank? b) Instead of (a), if 3000 litres of water are added to the tank, what is the final concentration of NaCl (expressed in mM)? c) Instead of (a) or (b), if an additional 500 litres of 25 mM...

(1 point) A bacteria culture starts with 560 bacteria and grows at a rate proportional to...

(1 point) A bacteria culture starts with 560 bacteria and grows at a rate proportional to its size. After 3 hours there will be 1680 bacteria. (a) Express the population after t hours as a function of t population: (function of t) (b) What will be the population after 2 hours? (c) How long will it take for the population to reach 1250 ?

A 200 litre tank initially contains water at 100 kPa and a quality of 1%. Heat...

A 200 litre tank initially contains water at 100 kPa and a quality of 1%. Heat is transferred to the water, thereby raising its pressure and temperature. At a pressure of 2 MPa, a safety valve opens, and saturated vapour at 2 MPa flows out. The process continues, maintaining 2 MPa inside until the quality in the tank is 90%, then stops. Determine the total mass if water that flowed out and the total heat transfer. *I’ve seen others have...

A tank contains 420 litres of a solution, with 20 kilograms of salt in the solution....

A tank contains 420 litres of a solution, with 20 kilograms of salt in the solution. A solution with a concentration of 57 kilograms per litre enters the tank at a rate of 7 litres per minute. The well-stirred solution flows out of the tank at the same rate. Determine the mathematical model that gives the function y(t), the number of kilograms of salt in the tank after t minutes

Subjects