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,

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