Thread: Population Growth problem

The rate of growth of dP/dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days.

dP/dt= k*sqrt t

The initial size of the population is 500. After 1 day, the population has grown to 600. Estimate the population after 7 days.

Hello,

Integrate both sides



for t=0 p=500
hence c=500

for t=1
p=2k/3+c=600
thus
k=150
-----------------------------------------------------
Try yourself now else see below
so
Now for 7 days
Population

Can you explain what k is in the problem? Is it just a variable for an unknown constant?

Originally Posted by yeloc

Can you explain what k is in the problem? Is it just a variable for an unknown constant?

k represents a constant whose value you have to find (actually I should use past tense since the value has been found).

Thank you adarsh and mr fantastic for the responses.