[填空题]
N is the population size of brown bears z-f 2- g ql;-teaof,uvin a forest, in units of 100 . At time f a-q; t2vez-lu, f-gobqi 4tk4sl jdcnt051 (q3zk-e t monthscl n-4ie0b(q4dqks 3 1ttj5kz, the rate of change of the population can be modelled by the differential equation
$\frac{\mathrm{d} N}{\mathrm{~d} t}=0.3 N-0.72 t$
1. Given that N=a+b t , for a, b $\in \mathbb{R}$ , is a solution to the differential equation 4 for a particular initial population, find the values of a and b .
a= ,b= .
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=6 .
3. Find the least value for N at t=0 that will ensure the population does not become extinct.
Therefore the minimum initial value for which population does not become extinct is N= .
A group of conservationists concerned with the brown bears extinction determines that the brown bear population will reach a maximum after six months and then begin to decline.
4. Write down an approximation for N at that time.
The conservationists decide to introduce more bears at t=6 months.we conclude the population at t=6 is .
5. If the model remains valid, find the least number of bears needed to be added for the population to continue to increase in the future.
Suppose that N=28 after 8 months.
6. Estimate N after 9 months by using Euler's method with a step size of 0.2 .
after 9 months
N≈ .(one decimal place)
