Answer:
The correct option is D.
Step-by-step explanation:
It is given that the population of bacteria begins with 1 bacterium and triples every hour.
Let initial population be 1.
[tex]P(0)=1[/tex]
The population of bacteria after 1 hour is
[tex]P(1)=1\times 3=3^1=3[/tex]
The population of bacteria after 2 hour is
[tex]P(2)=3\times 3=3^2=9\[/tex]
Similarly the population of bacteria after n hour is
[tex]P(n)=3\times 3\times ...\times 3=3^n[/tex]
If x is number of hours and y is the population of bacteria after x hour, then
[tex]y=3^x[/tex]
The other way to find the population model is shown below.
The population model is defined as
[tex]P=a(1+b)^x[/tex]
Where, a is initial population and (1+b) is growth factor.
In the given situation the initial population is 1 and growth factor is 3, therefore
[tex]y=3^x[/tex]
Therefore option D is correct.
