A population of 3000 bacteria is introduced into a culture and grows in number according to the formula
P(t)= 3000(1 + 3t/100+ t^2),
where t is measured in hours. Find the rate at which the population is growing when t=1
A population of 3000 bacteria is introduced into a culture and grows in number according to the formula
P(t)= 3000(1 + 3t/100+ t^2),
where t is measured in hours. Find the rate at which the population is growing when t=1
Well, the rate of which it's growing will be told by the derivative of the population equation.
so take the derivative of P(t):
P(t) simplified is: 3000+60t+3000t^2
derivative of P(t)=90+6000t
then plug in 1 for t
90+12000=12090
so when t=1 the population is growing at a rate of 62 bacteria per hour
(plug into calculator to check)
i'm pretty sure to find the rate when t = 1 you take the derivative of the original function
so P'(t)=3000(3/100 + 2t)
and plug in t = 1 and get 6090 bacteria/hr
i think thats the answer, i was struggling with this today and someone showed me how to do it. so i just learned it...