Mycobacterium tuberculosis increases in number at an hourly growth rate of 3.8 percent per hour.
When a certain critical number of bacteria are present in the lungs, a person is able to transmit the disease to others. If 10 bacteria infect a person, the critical level is reached in four weeks.

(a) How long will it take for the critical level (at which point the individual's illness becomes contagious) to be reached if the same person is infected with 20 bacteria?

Question

Mycobacterium tuberculosis increases in number at an hourly growth rate of 3.8 percent per hour. 
When a certain critical number of bacteria are present in the lungs, a person is able to transmit the disease to others. If 10 bacteria infect a person, the critical level is reached in four weeks.

(a) How long will it take for the critical level (at which point the individual's illness becomes contagious) to be reached if the same person is infected with 20 bacteria?