Avirus 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