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The population after 20 weeks will be 403.42 in which
is the initial population.
Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.
We are required to find the number of bacteria present after 10 weeks.
let the number of bacteria present at t is x.
So,
dx/dt∝x
dx/dt=kx
1/x dx=k dt
Now integrate both sides.
=
log x=kt+log c----------1
Put t=0
log =0 +log c (
shows the population in beginning)
Cancelling log from both sides.
c=
So put c= in 1
log x=kt+log
log x=log +log
log x=log
x=
We have been given that the population triples in a week so we have to put the value of x=2 and t=1 to get the value of k.
2=
2=
log 2=k
We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.
x=
x=
x=
x=403.42
Hence the population after 20 weeks will be 403.42 in which
is the initial population.
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The given question is incomplete as the question incudes the following:
Calculate the population after 20 weeks.