Hi guys, I really need your help! Ive been having trouble with these questions and if i dont complete them i will fail! Here are the questions below:
These questions are based around the survival rate of butterflies and the information is present:
Model 1
B = Butterflies
T = Years
Initial population = 300 butterflies
DB
dt = (p-q) B
p = positive constant related to birth rate
q = positive constant related to death rate
Question 1
When p = 0.10 and q = 0.05, Calculate the number of butterflies after T years
i) 10 years later
ii) 100 years later
Question 2
a) when 0.07<p<0.11 and 0.06<q<0.08
Find the number of butterflies after T years. With the combinations of p and q, sketch the graphs
b) find values of p & q when the population
i) remains stable
ii) increase without limit
iii) die out
c) comment on the limitations of the model
Model 2
A more sophisticated mathematical model for B after T years. The initial amount is still 300 Buttflys settled but tis time the food must be taken into account.
It is modelled with this equiation
dB
dt = (p-q-kB)B
p and q are again related with the reproduction and death rate, and k= positive constant related to the amount of food.
Question 3.
explain the effect of "-kB" that has on growth rate of the butterfly population.
Question 4.
suppose p=.10 and q=.05 and k=.00003 (model 2)
Find an expression for the number of butterflys on the island after t years.
According to this 2nd model, what would the butterfly population be 10 years and 100 years after the initial settlement? How does this compare with the first model?
At what time t is the butterfly population increasing rapadly?
Sketch a graph that shows how the butterfly population changes over the time in this case.
Comment on what the graph shows
Your Help is Appreciated!
These questions are based around the survival rate of butterflies and the information is present:
Model 1
B = Butterflies
T = Years
Initial population = 300 butterflies
DB
dt = (p-q) B
p = positive constant related to birth rate
q = positive constant related to death rate
Question 1
When p = 0.10 and q = 0.05, Calculate the number of butterflies after T years
i) 10 years later
ii) 100 years later
Question 2
a) when 0.07<p<0.11 and 0.06<q<0.08
Find the number of butterflies after T years. With the combinations of p and q, sketch the graphs
b) find values of p & q when the population
i) remains stable
ii) increase without limit
iii) die out
c) comment on the limitations of the model
Model 2
A more sophisticated mathematical model for B after T years. The initial amount is still 300 Buttflys settled but tis time the food must be taken into account.
It is modelled with this equiation
dB
dt = (p-q-kB)B
p and q are again related with the reproduction and death rate, and k= positive constant related to the amount of food.
Question 3.
explain the effect of "-kB" that has on growth rate of the butterfly population.
Question 4.
suppose p=.10 and q=.05 and k=.00003 (model 2)
Find an expression for the number of butterflys on the island after t years.
According to this 2nd model, what would the butterfly population be 10 years and 100 years after the initial settlement? How does this compare with the first model?
At what time t is the butterfly population increasing rapadly?
Sketch a graph that shows how the butterfly population changes over the time in this case.
Comment on what the graph shows
Your Help is Appreciated!
