A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find ho

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A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find ho

w 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.

Mathematics

2 answers:

IRISSAK [1] · Answer 1 · 2023-09-24T22:51:17+03:00

<h2>Hello!</h2>

The answer is: 23.77 hours

$Total(t)=Start*2^\frac{t}{15}$

Where:

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

<em>Start</em> is the original amount

<em>t </em>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:

$Total(15)=100*2^\frac{15}{15}=100*2^{1}=100*2=200$

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

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