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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.)

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JDcap

Answer:

5,274,027 bacteria

Step-by-step explanation:

First, we find the function of number of bacteria:

[tex]N(t)=400(450.262)\,e^{1.12567t}\\ N(t)=180104.8\,e^{1.12567t}[/tex]

Now, we replace t=3 and operate.

[tex] N(3) = 180104.8\,e^{1.12567(3)}=180104.8(29.2831)\\ N(3)=5274026.86888\approx 5274027[/tex]

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