Hey i have some revision questions that i'm having trouble with.

1. 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.

2. The department of civil aviation have strict rules concerning the heights of structures/airborne articles near an airport. A weather balloon is to be tethered to the ground by a 250m rope. Because of the air traffic regulations the balloons height must not exceed 200m. Throughout the day a clinometer is used to measure the angle of elevation to the nearest degree. At 1pm the angle was measure at 53 degrees. Can the weather people be sure the balloon's height is within regulations.

Verify your decision using a calculus method mentioning any pertinent assumptions.

Thanks in Advance