Question

A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours​

Answer 1

Answer:

24 hours

24 hours is the solution to 300=10(2)^t/15

Answer 2

After 24 hours the scientist expect to have 300 bacteria cells.

Given :

the number of cells to be given by the formula, where t is the number of hours since the experiment started.

$C=100(2)^{\frac{t}{15} }$

't' represents the time taken for the cells to grow.

we need to find out the time taken to have 300 bacteria cells.

So, we replace C with 300 and solve for t

$C=100(2)^{\frac{t}{15} }\\300=100(2)^{\frac{t}{15} }\\\frac{100\cdot \:2^{\frac{t}{15}}}{100}=\frac{300}{100}\\2^{\frac{t}{15}}=3\\\frac{t}{15}\ln \left(2\right)=\ln \left(3\right)\\t=\frac{15\ln \left(3\right)}{\ln \left(2\right)}\\t=23.77443$

So, it takes 24 hours to have 300 bacteria cells.

Learn more : brainly.com/question/11587654