Answer to Question #258045 in Functional Analysis for Artika

Question #258045

How fast is the size of the population changing after 1 minute? 


1
Expert's answer
2021-10-29T03:02:03-0400
P(t)=3t2+3et+10,t0P(t)=3t^2+3e^t+10, t\geq0

P(t)=(3t2+3et+10)=6t+3etP'(t)=(3t^2+3e^t+10)'=6t+3e^t

Given t=1 min=60 sec.t=1\ min=60\ sec.


P(60)=6(60)+3e60=360+e601.142×1026P'(60)=6(60)+3e^{60}=360+e^{60}\approx1.142\times10^{26}

The popukation increases at rate of 360+e601.142×1026360+e^{60}\approx1.142\times10^{26} bacteria per second after 1 minute.



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