Suppose a colony of bacteria grows exponentially, and suppose there are 100 bact

Question

Suppose a colony of bacteria grows exponentially, and suppose there are 100 bacteria at 12:35pm 1,000 bacteria at 12:36pm. Find c and b such that f(t) = c middot b^t, where t is the time (in minutes) elapsed since 12:35pm. How many bacteria will there be at 12:37pm? (For the remainder of these problems, I advise you try to solve without fitting a model f(t) = c middot b^t Suppose a (different) colony of bacteria grows exponentially, and there are 2,000 bacteria at l:40pm and 20,000 at 1:50pm. When will the population reach 200,000?

Explanation / Answer

7] f(t) = cbt

at t = 0, f(t) = 100

so, 100 = cbo

or c = 100

and at t = 1 min, f(t) = 1000

1000 = 100b1

b = 10

therefore, f(t) = 100 x 10t

b] f(t) = 100 x 102 = 10000.

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