Question

if a bacteria population starts with 100 bacteria and doubles after every 10 hours, how long it takes for the population to reach 10,000?

Answer 1

Hi,

`P_n=a*e^(b*n)\\P_0=100\ \Rightarrow\ 100=a*1\ \Rightarrow\ a=100\\\\P_10=200=100*e^(b*10)\\\Rightarrow\ e^(10*b)=2\\\Rightarrow\ b=(ln(2))/(10) \\P_n=100*e^(b*n)\geq 10000\\\Rightarrow\ b*n\geq\ ln(100)\\\\n\geq\ (10*ln(100) )/( ln(2) )\\\\n\geq\ 66.4385...\\\\\boxed{n\approx 67}`