Not sure how to solve this doubling time problem?

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1 Answer
Guillaume L.
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!

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