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I want to calculate the doubling time of coronavirus notifications, having a daily multiplier value of 1.24.

In other words, if the number of infections increases at 24% per day, how many days does it take for the number to double?

Other replies indicate a solution using log base 2, but I don't know how to solve this function.

everpom
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  • I did an analysis of the stats on confirmed US infections posted on www.corona.help with a similar result. Notice how the growth changes from country to country though. Roughly, I think that countries who are not doing strict quarantines are seeing exponential growth while those that are (China, South Korea) look more like logistic growth. So the global growth pattern is a little more complicated. – j0equ1nn Mar 23 '20 at 19:20
  • This hurts me that others have down-voted. In my mind, I see a student that is curious, exploring a world issue on his/her own time and trying to gain knowledge. Yes, it is a very simple question, but is that really a reason to downvote? Could someone please explain to me how this question lacks details/clarity? To me, it is a question that is perfectly summarized, and deserves an answer. I am inclined to believe the down-voters are being exclusionary and egotistical, and should reconsider the purpose of this site; while, I am open to criticism of this opinion. – MathsofData Mar 26 '20 at 05:30

1 Answers1

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You need to solve $1.24^n = 2$ and you can do that by taking logarithms of both sides.

$1.24^n = 2$

$\log 1.24^n = \log 2$

$n\log 1.24= \log 2$ (using the rules of logarithms)

$n = \frac{\log 2}{\log 1.24} \approx 3.22$.

At day $3$, it won't quite have doubled, at day $4$, it will have overshot. If you're looking for an integer number at which it's at least doubled, the answer is $4$.

It doesn't matter which base of logarithm you use, as long as it's the same throughout. You can use either LOG (base $10$) or LN (base $e$) on your calculator.

Deepak
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