SOLUTION: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria.      Log On


   

Question 1199264: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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    B(t) = B%5B0%5D%2Ae%5E%28r%2At%29

    500  = 100%2Ae%5E%28r%2A5%29

    500%2F100 = e%5E%285r%29

    5 = e%5E%285r%29

    ln(5) = ln%28e%5E%285r%29%29

    ln(5) = 5r

    r = ln%285%29%2F5 = 0.3218875... = 0.3119   (rounded).


ANSWER.  Exponential growth rate of the colony of bacteria is 0.3119 bacteria/hour.

Solved.