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
[tex]P'=kP[/tex] where k is constant of proportionality
separate the variables as
[tex]\frac{dP}{P} =kdt\\ln P =kt+C\\P = Ae^{kt}[/tex]
If after 1 hour population is B (say)
[tex]B=Ae^{k} \\\\k = ln B - ln A[/tex]
then k = ln B - ln A
Using this
P(t) = [tex]Ae^{(lnB-lnA)t}[/tex]
b) P(e) = [tex]Ae^{(lnB-lnA)3}[/tex]
c) Rate of growth = [tex](ln B- ln A)Ae^{(lnB-lnA)3}[/tex]
Unless you give B value, d cannot be solved
