Question

A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.262)e1.12567t bacteria per hour. how many bacteria will there be after three hours? (round your answer to the nearest integer.)

Answer 1

The bacteria population given by the exponential function r(t) = (450.262)e1.12567t would be approximately 3984665 bacteria after three hours.

Step-by-step explanation:

The subject of the question is mathematics, specifically, it's about exponential growth, which is a common topic in high school algebra. The bacteria population is given by an exponential function r(t) = (450.262)e1.12567t, which represents continuous compounding of growth. To find the bacteria population after three hours, we must substitute t = 3 into this equation.

Then we have r(3) = (450.262)e1.12567*3 = 3984664.65. Since we can't have a fraction of a bacterium, we approximate the population to the nearest integer. So, the bacteria population after three hours would be approximately 3984665 bacteria.

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