Question

A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function to model the situation. (Exponential Growth and Decay)​

Answer 1

The function is written as: The function
`p(x) = 50 * 2^x`

How to create the function

To model the situation where a species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes, we can use the formula for exponential growth:

`f(x) = \text{initial number of cells} * 2^{\text{(x/number of time periods for doubling)}}`

Here, the initial number of cells is 50, and the number of time periods for doubling is 1, since the bacteria doubles in number every 30 minutes. Therefore, the function to model this situation is:

`f(x) = 50 * 2^((x/1 )) = 50 * 2^x`

So, if x is the number of 30-minute time periods, then f(x) gives us the number of cells in the culture after x time periods.