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

Question

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 = ?

Answer 1

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

Answer 2

a.) f(t)= 480t
b.) f(3)= 480(3) = 1440
c.)1550= 480t
t=3.229 hours

Answer 3

y(t) = 480 * 2^(t/2)
y(3) = 1357
T = 3.4 h