Apopulation of bacteria is initially 6000. after three hours the population is 3000. if this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours.

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  p(t) = 6000·(1/2)^(t/3)

Step-by-step explanation:

An exponential growth or decay can be modeled by ...

  value = (initial value) · (growth factor)^(t/(time for growth factor))

Here, the growth factor is 3000/6000 = 1/2 in 3 hours. The initial value is 6000. Putting those numbers into the above form, we have ...

  p(t) = 6000·(1/2)^(t/3)

If you prefer your exponential functions to be a power of e, then this is ...

  p(t) = 6000·e^(-0.23105t)

The constant -0.23105 is ln(1/2)/3.