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Answer:
There are 81,377,396 bacteria in the population after 4 hours. The population reaches 100 million bacteria after 244.12 minutes.
Step-by-step explanation:
Systems that exhibit exponential growth increase according to the mathematical model
y={y}_{0}{e}^{kt},
where {y}_{0} represents the initial state of the system and k>0 is a constant, called the growth constant.
We have f(t)=200{e}^{0.02t}. Then
f(300)=200{e}^{0.02(300)}\approx 80,686.
There are 80,686 bacteria in the population after 5 hours.
To find when the population reaches 100,000 bacteria, we solve the equation
The population reaches 100,000 bacteria after 310.73 minutes.