Ask Question
27 January, 03:52

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 570. (a) Find an expression for the number of bacteria after t hours. P (t)

+1
Answers (1)
  1. 27 January, 07:39
    0
    p (t) = 100e^ln5.7t

    Explanation:

    The growth rate of bacteria is directly proportional to its size and shows the exponential growth. The initial bacteria amount is 100 and later increased to 570.

    The number of bacteria after t hours is

    p (t) = 100e^kt where k is the relative growth rate. and t is the time.

    Here p (t) = 570 and t = 1 hour, then K =

    420=100e^k (1)

    K = ln (5.7)

    Put the value of K in original equation then,

    p (t) = 100e^ln (5.7) t

    Thus, the expression for the number of bacteria after t hours is p (t) = 100e^ln (5.7) t.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to ...” in 📘 Biology if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers