in a scientific study, the size , p of a population at t hours is being studied. Initially p = 560 and after 6 hours, p is found to be 1218. In a simple model of population growth, the rate of the population is taken to be proportional to the population at that time. Using this model predict.(adsbygoogle = window.adsbygoogle || []).push({});

a) the size of the population 24 hours after the start of the experiment.

b) how long it will take for the population to increase tenfold.

I keep getting the wrong answer, here's my working any help appreciated.

[tex] \frac{dp}{dt} = kt [/tex]

[tex] \int \frac{1}{p} dp = \int k dt [/tex]

[tex] ln (p) = kt +c [/tex]

[tex] p = p_{0}e^{kt} [/tex] p_{0} = 560 , t= 0

[tex] p = 560e^{kt} [/tex]

[tex] 1218 = 560e^{k6} [/tex]

[tex] k = ln(\frac{1218}{3360}) [/tex]

so to find after 24 hours I would just put t = 42 into my formula, and get ;

[tex] p = 560e^{ln\frac{1218}{3360}24} [/tex]

But when I solve this I get 4872, and the correct answer is 12532

What am I doing wrong?

Thank you.

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# Homework Help: Differential equations help, modelling population

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