SOLUTION: A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 3 hours there will be 480 bacteria.
(a) Express the population P after t hours as
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Question 1179719: A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 3 hours there will be 480 bacteria.
(a) Express the population P after t hours as a function of t.
P(t)=
(b) What will be the population after 4 hours?
(c) How long will it take for the population to reach 2770? Round your answer to two decimal places.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size.
After 3 hours there will be 480 bacteria.
(a) Express the population P after t hours as a function of t.
, where
P(t) = 480
p = 160
t = 3
k = constant
using logs
3k*ln(2) = ln(3)
3k =
3k = 1.585
k =
k = .528
The equation
:
(b) What will be the population after 4 hours?
p(t) = 692
:
(c) How long will it take for the population to reach 2770?
Round your answer to two decimal places.
.528t =
.528t = 4.1137
t =
t = 7.79 hrs
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