Science:Math Exam Resources/Courses/MATH110/December 2014/Question 08 (a)
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Question 08 (a)
Assume that the number of bacteria at time (in minutes) follows an exponential growth model , where and are constant. Suppose the count in the bacteria culture was 300 after 15 minutes and 1800 after 40 minutes. You may leave your answers unsimplified, i.e. in "calculator-ready" form.
(a) What was the initial size of the culture?
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Find the constant by using the given information.
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Since the count in the bacteria culture was 300 after 15 minutes and 1800 after 40 minutes, this means and .
This implies that
Then dividing by , we get
Solving , we get and hence .
Plugging this back into the equation , we can find .
Therefore, the initial size of culture .