Question

The population of bacteria in a culture doubles every 14 hours. How long will it take for

the population to triple?

Answer 1

Answer: 22 hours 11 minutes

Explanation:

`P=P_o\cdot e^((kt))\\\\\text{Since the initial population is doubled in 14 hours, then:}\\2P_o=P_o\cdot e^(k\cdot 14)\\2=e^(14k)\\ln\ 2=ln\ e^(14k)\\ln\ 2=14k\\\\(ln\ 2)/(14)=k\\\\0.0495=k\\\\\\\text{Now that the k-value has been determined, we can find the time when the}\\\text{population is tripled:}\\3P_o=P_o\cdot e^(0.0495t)\\3=e^(0.0495t)\\ln\ 3=ln\ e^(0.0495t)\\ln\ 3=0.0495t\\\\(ln\ 3)/(0.0495)=5\\\\22.19=t\\\\22\ hrs +0.19\ hrs`

`22\ hours + \bigg[(19)/(100)=(x)/(60)\bigg]\\\\22\ hours + 11\ minutes`