The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 16% per hour. Suppose that a sample culture has an initial population of 71 bacteria. Find the predicted population after three hours Do not round any intermediate computations, and round your answer to the nearest tenth bacteria .

Answer:

114.7

Explanation:

A (t) represent the population of the bacteria at the time t.

Since, the population grows exponentially, the population can be calculated as follows:

A (t) = Ao × $e^{kt}$

A (t) is teh final population, Ao is the initial population, e is the exponential, k is rate and t is time.

A (t) = 71 × $e^{0.16\times t}$

For t = 3 hours

A (t) = 71 × $e^{0.16\times 3}$

A (t) = 114.7.

The population of bacteria after 3 hours is 114.7.

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