According to the question,
dtdP=kP where P is population at any time
solving equation,
∫PdP=∫kdt
lnP=kt+C (1)
Applying the conditions,
at t=0, P = 500
ln500=C (2)
at t=10, P= 575
ln(575)=k(10)+ln(500)
k=101ln(500575)=0.0139762
So Equation of the Population growth is given by
P=500e0.0139762t (3)
Population in 50 years,
P=500e0.0139762∗50=1005.6≈1006 people
Rate of population growth is
dtdP=dtd(500e0.0139762t)=(500∗0.0139762)e0.0139762t
putting t = 50, we get
dtdP=(500∗0.0139762)e0.0139762∗50=14 people/year (approx)
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Dear Kabilen, please use the panel for submitting new questions.
The population of a town grows at a rate proportional to the population present at time t. The initial population of 5000 increases by 50% in 10 years. What will be the population in 30 years?
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