Answer:
Options A and B are true
Step-by-step explanation:
In this question it is given that population of a bacterial colony doubles every 10 minutes and the function that represents the number of bacteria in colony after x minutes is [tex]3.(2)^{\frac{x}{10} }[/tex]
Now we check each option given
A. The expression [tex](2)^{\frac{x}{10} }[/tex] reveals the population of the bacterial colony increases by 100% every 10 minutes.
Let's check by putting x = 10
[tex]3.(2)^{\frac{10}{10}}=(3).(2) = 6[/tex]
Here after 10 minutes initial population which was 3 got doubled to 6. So option A is true.
B. Expression [tex](1.07)^{x}[/tex] reveals the approximate rate of increase in the population of the bacterial colony per minute.
Let's solve the expression
[tex]3.(2)^{\frac{x}{10}}=3.[(2)^{\frac{1}{10}}]^{x}=3.[1.07]^{x}[/tex]
Option B is true.
C. This option is not correct as we have already solved the expression in option B.
D. This option can't be correct because it is itself given in the question that [tex](2)^{\frac{x}{10}}[/tex] reveals that the bacterial colony increases by 100% in 10 minutes.
E. Let's check this option by putting x = 1 minute in [tex]3.(2)^{\frac{x}{10} }[/tex]
and in [tex](1024)^{x}[/tex] . If solutions of both the expressions are same then this option will be correct.
[tex]3.(2)^{\frac{x}{10} }=3.(2)\frac{1}{10}=3.(1.07)=3.21[/tex]
And [tex](1024)^{x}=(1024)^{1}=1024[/tex]
As both the solutions are different so Option E is incorrect.
F. As we have seen in option E both the expressions give different values for different values of x so Option F will be incorrect again.
Options A and B are true.
