Answer:
See Attachment
Step-by-step explanation:
The graph of Y=5.5x will be a straight line passing through origin as shown in attachment.
Step-by-step explanation:
just think it through :
0.4x + 20 < 200
0.4x < 180
x < 180/0.4 = 450
so, x < 450
they must order less than 450 bars.
therefore, the first answer option is correct :
they can order from 0 to 449 bars, but no more.
The number of people that own pets???
Answer:
a) dx/dt = kx*(M - h/k - x)
Step-by-step explanation:
Given:
- The harvest differential Equation is:
dx/dt = kx*(M-x)
Suppose that we modify our harvesting. That is we will only harvest an amount proportional to current population.In other words we harvest hx per unit of time for some h > 0
Find:
a) Construct the differential equation.
b) Show that if kM > h, then the equation is still logistic.
c) What happens when kM < h?
Solution:
- The logistic equation with harvesting that is proportional to population is:
dx/dt = kx*(M-x) hx
It can be simplified to:
dx/dt = kx*(M - h/k - x)
- If kM > h, then we can introduce M_n=M -h/k >0, so that:
dx/dt = kx*(M_n - x)
Hence, This equation is logistic because M_n >0
- If kM < h, then M_n <0. There are two critical points x= 0 and x = M_n < 0. Since, kx*(M_n - x) < 0 for all x<0 then the population will tend to zero for all initial conditions
