# Exponential growth percentage conversion

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!

• 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. Commented Apr 5, 2022 at 10:39
• 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. Commented Apr 5, 2022 at 10:41
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).