A certain culture of 2,000 bacteria grows to a population of 24000 in 3.5 hours. How long will it take culture of 2000 bacteria to grow to a population of 1000000

Answer 1

Hi there! I'd love to help you out....

When dealing with any type of population growth (including bacteria) we use the formula:

A = Pe^(rt) where P = initial population, r = rate of growth, and t = time (e is Euler's number).

For this problem, we need to figure out the rate of growth by plugging in the first set of numbers we are given:

24000 = 2000 e ^(r * 3.5) Now we solve for r:

24000 / 2000 = e ^(r*3.5)

12 = e ^ (r * 3.5)

ln(12) = r * 3.5

[ ln (12)] / 3.5 = r

0.70997 = r

We now know our rate of growth is approximately 71% (we find this by multiplying the r we found by 100). We can use this in place of "r" going forward. Now for this next part, we want to know the time it takes to take the same colony of bacteria to grow to 1000000 which means this time we will be solving for "t":

1000000 = 2000 e ^ (0.70997 * t)

1000000 / 2000 = e ^(0.70997 * t)

500 = e ^ (0.70997 * t)

ln(500) = 0.70997 * t

[ln (500)] / 0.70997 = t

8.75 hours = t

So, it will take our colony of bacteria 8.75 hours to grow to a population of 1,000,000. I hope this explanation was thorough and answered all of your questions. If you have additional questions, please don't hesitate to reach out! Learn on! :)