[填空题]
Suppose the populatio;tmfi95v2 u3 3uxcjbmop0gm5n size of a bee colony in units of g+t xqm9a5t.* ng rig/10 is N . At time t weeks, the rate of change of th+i5tg mg.an*q9xrt/g e population can be modelled by the differential equation $\frac{\mathrm{d} N}{\mathrm{~d} t}$=0.4 N-0.8 t
1. Given that N=a+b t , for a, b $\in \mathbb{R}$ , is a solution to the differential equation for a particular initial population, find the values of a and b .
a= .
The slope field for the differential equation is shown below
2. Sketch on the slope diagram:
1. the line N=a+b t
2. the trajectory of the population if at t=0, N=3 .
3. Find the least value for N at t=0 that will ensure the population does not become extinct.
N= .
A beekeeper measuring the population N determines it will reach a maximum after two and a half weeks and then will begin to decline.
4. Write down an approximation for N at that time.
The beekeeper decides to introduce more bees at t=2.5 .
5. If the model remains valid, find the least number of bees N that needs to be added in order for the population to continue to increase in size as time increases.
Therefore, the beekeeper needs to increase N by .
Suppose that N=80 after 4 weeks.
6. Estimate N after 5 weeks by using Euler's method with a step size of 0.2 .
N≈ .
