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The question states:

If bacteria is doubling in size every 20 minutes, at what % rate is the number of bacteria increasing every hour?

So firstly using the rule of 70, I approximated that the percentage growth rate is 3.5%. This is however every minute. How do I convert it to every hour, should I just multiply it by 60? Thank you!

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2 Answers 2

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If bacteria is doubling in size every 20 minutes, what about the size after 40 minutes?, and after 60 minutes?

Hope this helps.

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  • $\begingroup$ Well in 60 minutes it's a factor of 8 right? So then 8 = (1+r) so r = 7, thus p = 700%. Is there a way tho how to convert it from minutes (3.5%) to hours (700%) such that I am able to use the rule of 70 in the beginning? $\endgroup$
    – Sam333
    Commented Apr 5, 2022 at 10:21
  • $\begingroup$ Yes, after one hour the size increases by a factor of 8. That is the exact solution (equivalent to a 700 % growth). $\endgroup$
    – G Frazao
    Commented Apr 5, 2022 at 10:30
  • $\begingroup$ I'm not familiar with the rule of 70, if I understand correctly, it is used to obtain a rough estimate of the doubling time, given a growth rate. However, in this case, you can compute the exact solution. $\endgroup$
    – G Frazao
    Commented Apr 5, 2022 at 10:31
  • $\begingroup$ After a quick google, I'm guessing the rule of 70 should apply to low % growth rates. $time to double = \frac{70}{growth rate}$ Example 1: with an hourly rate of 70 %, the rule of 70 gives you a doubling time of 1 hour, which is not accurate. $\endgroup$
    – G Frazao
    Commented Apr 5, 2022 at 10:39
  • $\begingroup$ Example 2: If you input $1/3$ hours as "time to double", the rule of 70 gives you an hourly growth rate of $210 \%$ which is far away from the exact answer. $\endgroup$
    – G Frazao
    Commented Apr 5, 2022 at 10:41
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Basically, after every $20$ minutes, the bacteria would double in size. This would mean that since $60=20\times3$, so the size of the bacteria after the $60$ minutes would be $2^3=8$ times the size of the bacteria before the $60$ minutes. But the question asks for the percentage, so it should probably be $800-100=700\%$, because it asks for the growth, and not the entire comparison (if you know what I mean).

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