ANSWER
The size of the bacteria after 100 minutes is 20158.7 bacteria
EXPLANATION
Given that;
The initial amount of bacteria is 2000
The size of the bacteria doubles every 1/2 hour
Apply the formula below to find the size of the bacteria for 100 minutes
[tex]\text{ P = P \lparen2\rparen}^t[/tex]Recall, that 1/2 hour is equivalent to 30 minutes
[tex]\begin{gathered} \text{ Convert 100 minutes to hours} \\ \text{ }\frac{100}{30}\text{ = 3.333 hrs} \end{gathered}[/tex]The population after 100 minutes is calculated below as
[tex]\begin{gathered} \text{ P = 2000 }\times\text{ \lparen2\rparen}^{3.333} \\ \text{ P = 2000 }\times\text{ 10.079} \\ \text{ P = 20158.7 bacteria } \end{gathered}[/tex]Therefore, the size of the bacteria after 100 minutes is 20158.7 bacteria
