A pond containing 4 cubic km of water has an initial pollutant concentration of
ID: 3009514 • Letter: A
Question
A pond containing 4 cubic km of water has an initial pollutant concentration of 200 kg/km^3. Relatively clean water containing 2 kg/km^3 of pollutant flows into the pond at a rate of .02 km^3/month. An ill considered irrigation system drains water from the pond at a rate of .04 km^3/month. Write a differential equation and an initial condition that can be used to model the rate of change of pollutant with time A cup of coffee, initially at 84 degree C, sits in a room with constant temperature 20 degree C. If the constant of proportionality k is .05, write a differential equation and an initial condition that models the rate of cooling of the coffee. A population with a growth rate of 0.9 births per person per year and a death rate of 0.3 deaths per person per year initially starts out with 200 members. Write a differential equation and an initial condition that models the rate of population change with time. A 90-volt electromotive force (EMF) is applied to an LR series circuit in which the inductance is 0.3 henry and the resistance is 900 ohms. Write a differential equation and an initial condition that models the rate of change of current with time. Prior to the application of the EMF there is no current flowing through the circuit.Explanation / Answer
A)POLLUTANT initial in pond
= 200*4 = 800 kg
let C(t) be amount of pollutant at time t
C'(t) = amount coming in - amount going out
= 2 * 0.02 - C(t) /V(t) *0.04
where V(t) is volume of pond at time t months
= 4 - 0.04*t + 0.02t = 4- 0.02t
So C'(t) = 0.04 - C/(4-0.02t) *0.04
C(0) = 800
b) T(0 ) = initital temperature = 84
T'(t) = -0.05(T(t) - 20) = constant of proportainilty times difference in temperature
c)P(0) = 200
P'(t) = 0.9 P - 0.3P = 0.6P
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