The rate of decrease of the population of a species is inversely proportional to the size of the population. 10 years ago there were 100, and 5 years ago that had dropped to 80. What is it now and how long until the species goes extinct? ..........I think I need to do some integration, but I'm lost as to the equation I need to write.
Rate of decrease in population
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integration
1 Answers
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If the population is $n$, rate of decrease is $\frac {dn}{dt}$ so you are given $$\frac {dn}{dt}=-\frac kn$$ where $k$ is the proportionality constant. You are given $n(0)$ and $n(5)$ and should be able to evaluate $k$ from that.