Question $4$: $20$ Marks

Consider the model

$\frac{dP}{dt}=7P+14P^2$

where $P(t)$ represents the size $of$ the population $at$ time $t.$

$(4\mathrm{.}1)Is$ this a logistic model? Justify your answer!

$(4\mathrm{.}2)$ Draw a phase line $of$ the model.

$(4\mathrm{.}3)$ Draw a sketch $of$ the solution curve $P(t),ifP(0)=7.$

Question $5$: $14$ Marks

Assume that for the system

$\frac{dx}{dt}=G(x)$

a graph $of$ the function $G$ looks like this:

$(5\mathrm{.}1)$ Draw a rough graph $of$ what the function $G(x)$ could look like.

$(5\mathrm{.}2)$ Draw a rough sketch $of$ the solution curves $x(t)$ when the initial value $isx(0)=1$ and when

the initial value $isx(0)=0.$