A bacteria population is 7000 at time t = 0 and its rate of growth is 1000 · 2t bacteria per hour after t hours. What is the population after one hour? (Round your answer to the nearest whole number.)
Question
A bacteria population is 7000 at time t = 0 and its rate of growth is 1000 · 2t bacteria per hour after t hours. What is the population after one hour? (Round your answer to the nearest whole number.)
Solution
The rate of growth of the bacteria is given by 1000 · 2^t.
At t = 1 hour, the rate of growth is 1000 · 2^1 = 2000 bacteria per hour.
This means that in one hour, the bacteria population increases by 2000.
So, the population after one hour is the initial population plus the increase, which is 7000 + 2000 = 9000.
Therefore, the bacteria population after one hour is 9000.
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