Question

A bacteria culture initially contains cells and grows at a rate proportional to its size. After an hour the population has increased to . (a) Find an expression for the number of bacteria after
hours.(b) Find the number of bacteria after 3 hours.(c) Find the rate of growth after 3 hours.(d) When will the population reach 10,000?

Answer 1

Answer:

Step-by-step explanation:

given that a  bacteria culture initially contains cells and grows at a rate proportional to its size.

If P be the size then growth rate

$P'=kP$ where k is constant of proportionality

separate the variables as

$\frac{dP}{P} =kdt\\ln P =kt+C\\P = Ae^{kt}$

If after 1 hour population is B (say)

$B=Ae^{k} \\\\k = ln B - ln A$

then k = ln B - ln A

Using this

P(t) = $Ae^{(lnB-lnA)t}$

b) P(e) = $Ae^{(lnB-lnA)3}$

c) Rate of growth = $(ln B- ln A)Ae^{(lnB-lnA)3}$

Unless you give B value, d cannot be solved