P is decreasing when P is in
Think about what these conditions mean for the population, and be sure that you are able to explain that.
In the long-run, what is the most likely outcome for the population?
P ?
(Enter infinity if the population grows without bound.)
Are there any inflection points in the solutions for the population? If so, give them as a comma-separated list (e.g., 1,3); if not, enter none.
Inflection points are at P =
Be sure you can explain what the meaning of the inflection points is for the population.
(d) Sketch a graph of $\frac{dP}{dt}$ against P. Use your graph to answer the following questions.
When is $\frac{dP}{dt}$ positive?
When P is in
When is $\frac{dP}{dt}$ negative?
When P is in
(Give your answers as intervals or a list of intervals.)
When is $\frac{dP}{dt}$ zero?
When P =
(If there is more than one answer, give a list of answers, e.g., 1,2.)
When is $\frac{dP}{dt}$ at a maximum?
When P =
Be sure that you can see how the shape of your graph of $\frac{dP}{dt}$ explains the shape of solution curves to the differential equation.
