Initially a population contains 1000 individuals. After t minutes the number N of individuals in the populataion is such that dN/dt = -0.25N.
a) write down the expression for N in terms of t
b) Find the rate at which the population is decreasing when it is half its orginal size.
This question is driving me nuts Any help would be much appreciated thanks
Reguards, Luke
actually now that i think about part (b), i think i probably would do it a different way. this way i get the answer to be -125, which is a thousand times what we got the answer to be last time, so we can't get away with, "no, professor, that's what i meant to write, it may just be a rounding off error, i deserve full credit!" hopefully this is right.
Now, for an exponential decay, which is what is happening here, this population seems to be dying out, we can find the half-life, that is, the time taken for half the original amount to remain, using the following formula:
, where is the half-life, is the rate of decrease. but let's see how this formula came about in the first place.
We want to find first, the time when the population reaches half its original amount, that is, when
we want
...look familiar?
Now
when :