Question

A bacterial population B is known to have
a rate of growth proportional to B itself. if be
between noon and 2pm, the population triples
at what time control being exerted, should
B become 100 times what it was at noon​

Answer 1

Step-by-step explanation:

It hampers the development of a country. It leads to the consumption of the natural resources at a much faster rate.

The fossils consumed, the resources depleted, the forests cleared, the heat produced,

the global warming caused are all the repercussions of the fast- growing population

Answer 2

At 8 PM ( approx )

Step-by-step explanation:

Let P represents the population of bacteria,

∵ the rate of growth of B is proportional to B itself,

i.e.

$\frac{dP}{dt}\propto P$

$\frac{dP}{dt}=kP$

$\frac{dP}{P}=kdt$

Integrating both sides,

$\ln P = kt + C$

$P=e^{kt+C}$

$P=e^{kt} e^C$

$P=P_0 e^{kt}$

Consider the population is estimated since noon,

Thus, at noon population,

$P=P_0 e^{0}=P_0$

Now, according to the question,

At 2 pm the population triples,

$3P_0=P_0 e^{2k}$

$3=e^{2k}$

Taking ln both sides,

$\ln 3 = 2k$

$\implies k =\frac{\ln 3}{2}\approx 0.549$

Now,

$100P_0 = P_0 e^{0.549t}$

$100=e^{0.549t}$

Taking ln both sides,

$\ln 100 = 0.549t$

$\implies t =\frac{\ln 100}{0.549}\approx 8$

Hence, at 8 PM, B will become 100 times what it was at noon​.

#Learn more:

A trend was observed in the growth of population in Saya Islands. The population tripled every month. Initially the population of Saya Islands was 100. what would be population after 4 months ?

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