Let a = x2 + 4Rewrite the following equation in terms of a and set it equal to zero (x2+4)2+32=12x2+48
1 answer:
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Solution:
Given :
.............(1)
where, B = aP = birth rate
D = = death rate
Now initial population at t = 0, we have
= 220 ,
= 9 ,
= 15
Now equation (1) can be written as :
.................(2)
Now this equation is similar to the logistic differential equation which is ,
where M = limiting population / carrying capacity
This gives us M = a/b
Now we can find the value of a and b at t=0 and substitute for M
and
So,
=
= 132
Now from equation (2), we get the constants
k = b =
=
The population P(t) from logistic equation is calculated by :
As per question, P(t) = 110% of M
Now taking natural logs on both the sides we get
t = 36.216
Number of months = 36.216