Question
In: Math
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
milcah answered 2 years agoRelated 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...
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?
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
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