I need help forming an equation for this word problem:

Question

An infectious strain of bacteria increases in number at a rate of 200%. There needs to be a certain number of bacteria for a person to become ill. If a person starts out with one bacterium, they will become ill in 36 hours. How long will it take a person to become ill if they are infected with 15 bacteria?

I only need an equation, the rest I can do :)

Answer 1

triples every hour = 200% hourly increase

in 36 hours

b=3^36=1.50094635 x 10^17 when they fall ill

set b above = 15(3^t)= 1.50094635 x 10^17

solve for t

3^t=1.0006309 x 10^16

log₃(3^t)= t = log₃(1.0006309 x 10^16)= ln(1.0006309 x 10^16)/ln3= about 33.535 hours

t= about 33 1/2 hours

= about 33 hours 32 minutes and 6 seconds