Question 998640: Please help. Show step by step. Thanks
A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there will be 1500 bacteria.
(a) Express the population P after t hours as a function of t .
P(t) =
(b) What will be the population after 5 hours?
bacteria
(c) How long will it take for the population to reach 2130? Give your answer accurate to at least 2 decimal places.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! That is what we cal exponential growth.
We like to express it as
 based on
 = the initial population,
 = a rate constant that we will find, and
 = and irrational number.
We could use any other base, as in
 , with a power of base  ,
and a different constant  .
However, we really like to use the number as a base,
because it makes the growth rate
 ,
making the ratio of the growth rate to the population size.
(a) So, with  and  ,
 --> --> --> --> , and
 <--> <-->
(b)  (rounded)
(c)  --> --> --> --> --> --> (rounded)
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