A population of bacteria is initially 2,000. After three hours the population is 1,000. Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t).

Step-by-step explanation:

The exponential formula for the size of the bacteria population after t hours is given by:

In which is the initial population and r is the rate which the population changes.

A population of bacteria is initially 2,000.

This means that

After three hours the population is 1,000.

This means that

So

Find the exponential function that represents the size of the bacteria population after t hours.

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