Please help these are calculus revision question for a final exam coming up soon.
Solve each of the following differential equations to find the corresponding growth function. (show all necessary calculus)
i. dQ/dt=kQ where k>0 t>= 0 Q(0)= Qo
2. A koala population N is subject to a birth rate a and a deah rate of b+y p per head of population per annum. Ecologists have modelled the rate of change of this population over time using the following:
dN/dt = (a-b)N-yN^2
It is knowln that a = 0.2, b=0.04, y= 2x10^-4 and the initial population was 200.
Determine if and when the population will have doubled in size.
I have this question down to t= int(1/(0.16N-2*1-^-4N^2) dn. I can't seem to integrate it properly. If someone could integrate and point me in the right direction for the rest of the question that'd be great.
Another derivitives question for a homework sheet.
The ends of a 4m long water trough are equilateral triangles whose sides are a metre in length.
If water is being pumped into the trough at a rate of 1.5m^3 / min find the rate at which the water level is rising when the depth is 30 cm.