course Mth 271
Week 3 quiz #3Write 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?
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I am not completely sure what to do with this one……I know that when you proportional it means y= kx^3 or y= kx^2
And I know that by rate you mean y= 2(a)(x) +(b)(x)
I don’t really know how to use this stuff to get what I am looking for…..so this is about all I can do with this one….Thanks!
300= 2954 x^3
300/2954= x^3
x= .467
y= 2954 * 0
=0
y= 2954 * 1.2^3
=5104.5
y= 2954 * 2.4^3
=40836.1
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The rate of change of population with respect to clock time is expressed as dP/dt.
A quantity is proportional to another if there exists a constant number k such that one quantity is k times the other.
So the equation would be
dP/dt = k P.