Not sure how to solve this doubling time problem?

enter image source here

1 Answer
May 10, 2018

t=ln(2)/ln(1.3)
t≈2.46

Explanation:

Let answer the first question. We know that each hour, the population of bacteria growth by 30%.
The population starts with 100 bacterias.
So after t=1 hour, we have 100*1.3=130 bacterias, and at t=2 hours, we have 130*1.3=169 bacterias, etc. So, we can define P(t)=100*1.3^t, where t is the number of hours.
Now, we search t where P(t)=200
So we have 100*1.3^t=200
1.3^t=2
ln(1.3^t)=ln(2)
Because ln(b^a) =alnb,
tln(1.3)=ln(2)
t=ln(2)/ln(1.3)
t≈2.46 hours
\0/ here's our answer!