Answer:
240
Step-by-step explanation:
According to law of exponential growth,
[tex]y=y_0e^{kt}[/tex]
Here, [tex]y_0[/tex] denotes the initial amount and k is the rate constant of the equation.
Now, the initial population is 240 bacteria.
Put [tex]y_0=240[/tex]
So,
[tex]y=240e^{kt}[/tex]
The population after 12 hours is double the population after 1 hour.
[tex]y(12)=2y(1)[/tex]
[tex]240e^{12k}=240e^{k} \\e^{12k}=e^{k} \\e^{12k-k}=1\\e^{11k}=1\\11k=log 1=0\\k=0[/tex]
(Formulae used: [tex]\frac{e^x}{e^y}=e^{x-y}\,,\,log 1=0[/tex])
So,
[tex]y=240e^{0}=240\\y=240[/tex]
Therefore,
Number of bacteria after 3 hours = 240
