• anonymous
A population grows exponentially according to the differential equation dP/dt = kP, where P is the population, t is time, and k is a positive constant. If P(0) = A, what is the time for the population to triple its initial value?
  • Stacey Warren - Expert
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  • katieb
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  • triciaal
  • hartnn
dP/dt = kP This can be solved by variable separation method. (1/P) dP = k dt and Integrate both sides. We will have a constant of Integration, say C, that can be found using the initial Condition, P(0) = A which means plug in t=0, P =A, to get the value of C. Lastly, we need when the population triples its initial value, so we need when P becomes 3A. Just plug in P=3A to get 't' which will be your answer :)

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