You have,Originally Posted by JohnSena
Divide sides by 25,
Take, logarithm
Thus, the exponent "comes down"
Thus,
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Added by CaptainBlack
Please do not delete your questions after they have been solved.
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solutions.
a) the rate of growth of population is proportional to the existing population.Originally Posted by JohnSena
So the population satisfies this differential equation:
,
which has solution:
.
Now we are told that the population grows by per year, so
after one year the population is times its original value so:
,
so: (thats a natural log by the way).
hence:
.
Missing assumption needed to solve this is that the rate of growth of theOriginally Posted by JohnSena
population is proportional to the existing population. Hence the population
satisfies the diffrenetial equation:
,
which has solution:
Now we are told that the population doubles in 8 hours so:
,
so: , or: .
Therefore:
.
Now at time the population is 5 times its original value so:
,
so:
or laking logs:
,
or:
RonL