Hello,
Integrate both sides
for t=0 p=500
hence c=500
for t=1
p=2k/3+c=600
thus
k=150
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Try yourself now else see below
so
Now for 7 days
Population
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.