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A certain culture of the bacterium Rhodobacter sphaeroides initially has 30 bacteria and is observed to double every 4 hours.
(a) Find an exponential model n(t) = n02t/a
for the number of bacteria in the culture after t hours.
n(t) = (b) Estimate the number of bacteria after 17 hours. (Round your answer to the nearest whole number.)
bacteria
(c) After how many hours will the bacteria count reach 1 million? (Round your answer to one decimal place.)

Respuesta :

The amount of bacteria inside the cultures following t hours is predicted by the exponential function n(t) = n02t/a and is 60.1 hours.

A number of bacteria inside the culture following t hours may be predicted using an exponential model, n(t) = n02t/a. n(t) = 30•2t/4

b) how many germs are present after 17 hours.

Microorganism n(17) = 30•217/4 = 571 microorganisms

Will there be one million bacteria (c) hours 1,000,000 = 30•2t/4 100000/3 = 2t/4

100000/3 = 2t/4 log2(100000/3)

15.02467797 = t/4

t equals 60.1.

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