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course
7/24 9
Write the differential equation expressing the hypothesis that the rate of change of a population is proportional to the population P. Evaluate the proportionality constant if it is known that the when the population is 2954 its rate of change is known to be 300. If this is the t=0 state of the population, then approximately what will be the population at t = 1.2? What then will be the population at t = 2.4?
dP/dt = k(PFinal-PInitial)
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The rate of change is proportional to the population, not the difference between the population and some initial population.
So the equation is
dP/dt = k P
You have the right value for k, so
dP/dt = .102 P.
Hopefully you can use this to answer the remaining questions.
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300 = k(2954-0)
k = .102
I believe this is wrong. From the lecture in the temperature example we were giving a rate of change and the room temp and the current temperature so it was very easy to evaluate k.
I really can't figure out this problem I would appreciate a tip and I will resubmit.
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Clarification on the meaning of this equation vs. the meaning of the temperature equations:
For a population we expect that the more people, the more babies, so the rate of change is simply proportional to the population.
For an object at a different temperature from its surroundings, it's the difference in the two temperatures that determines how fast that object will warm up or cool down.
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