Question

Not sure how to solve this doubling time problem?

Answer 1

`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!