Question

A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number. It takes hours for the number of bacteria to increase to 300.

Answer 1

23.77

Explanation:

Answer 2

Hello!

The answer is: 23.77 hours

Why?

`Total(t)=Start*2^(t)/(15)`

Where:

Total(t) is equal to the amount for a determined time (in hours)

Start is the original amount

t is the time in hours.

For example, it's known from the statement that the bacteria double their population every 15 hours, so it can be written like this:

`Total(15)=100*2^(15)/(15)=100*2^(1)=100*2=200`

To calculate how long it takes for the bacteria cells to increase to 300, we should do the following calculation:

`300=100*2^{(t)/(15) } } \\(300)/(100)=2^{(t)/(15) } }\\log(3)=log(2^{(t)/(15) })\\\\\\log(3)=(t)/(15)*log2\\t=(log(3))/(log(2)) *15=23.77`

So, to know if we are right, let's replace 23.77 h in the equation:

Total(t)=100*2^\frac{23.77}{15}=299.94

and 299.94≅300

Have a nice day!