Question

A bacteria culture initially contains 2000 bacteria and doubles every half hour.A) Find the size of the baterial population after 100 minutes.B) Find the size of the baterial population after 10 hours.

Answer 1

The size of the bacteria after 100 minutes is 20158.7 bacteria

Step-by-step 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

`\text{ P = P \lparen2\rparen}^t`

Recall, that 1/2 hour is equivalent to 30 minutes

`\begin{gathered} \text{ Convert 100 minutes to hours} \\ \text{ }(100)/(30)\text{ = 3.333 hrs} \end{gathered}`

The population after 100 minutes is calculated below as

`\begin{gathered} \text{ P = 2000 }*\text{ \lparen2\rparen}^(3.333) \\ \text{ P = 2000 }*\text{ 10.079} \\ \text{ P = 20158.7 bacteria } \end{gathered}`

Therefore, the size of the bacteria after 100 minutes is 20158.7 bacteria