Ask Question
8 April, 13:25

The count in a bacteria culture was 300 after 15 minutes and 1300 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?

Find the doubling period?

Find the population after 105 minutes?

When will the population reach 12000

+1
Answers (1)
  1. 8 April, 13:50
    0
    Inicial size of the culture = 69.2246

    Doubling period = 7.0902 minutes

    Population after 105 minutes = 1,987,397.71

    Time for population reaches 12000: 52.7334 minutes

    Step-by-step explanation:

    First we need to find the exponencial function using the two information given. The model for an exponencial function is:

    P = Po * (1+r) ^t

    Where P is the final value, Po is the inicial value, r is the rate and t is the time. So we have that:

    300 = Po * (1+r) ^15

    1300 = Po * (1+r) ^30

    Isolating Po in both equations, we have that:

    300 / (1+r) ^15 = 1300 / (1+r) ^30

    (1+r) ^30 / (1+r) ^15 = 1300/300

    (1+r) ^15 = 4.3333

    1+r = 1.1027

    r = 0.1027

    From the first equation, we can use r to find Po:

    300 = Po * (1+0.1027) ^15

    Po = 300 / (1.1027) ^15 = 69.2246

    To find the doubling period, we have that P/Po = 2, so:

    (1+0.1027) ^t = 2

    log (1.1027^t) = log (2)

    t*log (1.1027) = log (2)

    t = log (2) / log (1.1027) = 7.0902 minutes

    The population after 105 minutes is:

    P = 69.2246 * (1+0.1027) ^105 = 1,987,397.71

    When the population reaches 12000:

    12000 = 69.2246 * (1+0.1027) ^t

    (1.1027) ^t = 12000/69.2246

    log (1.1027^t) = log (173.3488)

    t*log (1.1027) = log (173.3488)

    t = log (173.3488) / log (1.1027) = 52.7334 minutes
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The count in a bacteria culture was 300 after 15 minutes and 1300 after 30 minutes. Assuming the count grows exponentially, What was the ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers