A bacteria culture starts with 480 bacteria and grows at a rate propotional to its size.After 2 hours there ar

there are 960 bacteria.


(a) Find the population after t hours


y(t)=?


(b) Find the population after 3 hours.


y(3) = ?


(c) When will the population reach 1550 ?


T = ?

A bacteria culture starts with 480 bacteria and grows at a rate propotional to its size.After 2 hours there ar
In this problem, we will use the formula for uninhibited growth, which A=A0*e^(kt) where A is the new amount, A0 is the original amount, k is the rate of growth, and t is time. First lets find the rate of growth, k.





960=480e^(2k)


2=e^(2k)


ln(2)=2k


k=ln(2)/2





Then we can find y(t)





a)


y(t)=480e^(t*ln(2)/2)





b)


y(3)=480e^(3*ln(2)/2) = 1 358





c)


1550=480e^(t*ln(2)/2)


155/48=e^(t*ln(2)/2)


ln(155/48)=t*ln(2)/2


t=[2ln(155/48)]/ln(2)


t=3.38 hours
Reply:a.) f(t)= 480t


b.) f(3)= 480(3) = 1440


c.)1550= 480t


t=3.229 hours
Reply:y(t) = 480 * 2^(t/2)


y(3) = 1357


T = 3.4 h