SOLUTION: 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.

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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