Question

Bacteria A has an initial population of 500 and doubles every day, while bacteria b has an initial population of 50 and triples daily.


A) After how long will the population of B overtake the population of A?

Answer 1

so let a(t) be the Bacteria A
and let b(t) be the Bacteria B
so we have
a(t)=500*2^t
b(t)=50*3^t
so we want to know when b(t)>a(t)
so we get
50*3^t-500*2^t>0
divide by 50
3^t-10*2^t>0
3^t>10*2^t
divide by 2^t
(3/2)^t>10
use logarithm with base 3/2
t>lg(3/2,10)
so in terms of natural logarithm you have
t > ln(10)/ln(3/2)

Answer 2

which is equal to roughly 5.67 that is you can say after 6 days it will be

Answer 3

Got it, thank you!