A virus spreads continuously at a rate of 5% more infections per hour. How long will it take for 100 to be infected after 100 people are infected

At the rate of 5% per hour, time to take another 100 to get infected is essentially time to double the infection.

We can use the rule of 72 to get a quick rough estimate

time = 72/5=14.4 hours.

Exact value:

100 (1.05) ^t = 200

1.05^t=2

take log

t=log (2) / log (1.05)

= 14.21 hours