Answer:
Statement-1 is false
Statement-2 is True
Step-by-step explanation:
Given initially 50 bacteria present in perish dish.
Also, the population of bacteria gets tripled in every 8 hours.
Part-1
We can model this information in a function.
The population of bacteria after [tex]t[/tex] hours will be
[tex]f(x)=P_0\times3^{\frac{x}{8}[/tex]
Where [tex]P_0[/tex] is initial population of bacteria.
[tex]f(x)[/tex] is population of bacteria after [tex]x[/tex] hours
And [tex]x[/tex] is the time in hour.
So, plugging these value in equation we get,
[tex]P=50\times3^{\frac{x}{8}[/tex]
And Statement-1 has a function [tex]f(x)=3(50)^{\frac{x}{8} }[/tex]
That does not match with our function [tex]f(x)=50\times3^{\frac{x}{8}}[/tex]
So, Statement-1 is false.
Part-2
Now plug [tex]x=36[/tex] hours.
[tex]f(x)=50\times3^{\frac{x}{8}}\\x=36\\f(x)=50\times3^{\frac{36}{8}}\\f(x)=50\times3^{4.5}\\f(x)=50\times140.29\\f(x)=7014.805[/tex]
So, the population after [tex]x=36[/tex] hours is ≅[tex]7015[/tex] bacteria.
