Answer:
a) dP / dt = 0.15*P ( 1 - P/750) , r = 0.15 , K = 750
b) decreasing : ( - inf , 0 ) & ( 750 , inf )
increasing : ( 0 , 750 )
Step-by-step explanation:
Given:
- The standard for of logistic equation:
dP / dt = r*P( 1 - P/K)
Where, r and K are constants.
- The given experimental relation is:
dP / dt = 0.15*P - 0.0002*P^2
Find:
Rewrite the equation in the typical form to determine the intrinsic growth rate(r) and environmental carrying capacity (K).
For what values of P is the population increasing and decreasing? Write your answers in interval notation
Solution:
- First we will convert the given relation into standard form as follows:
dP / dt = 0.15*P - 0.0002*P^2
Factor out 0.15*P:
dP / dt = 0.15*P ( 1 - P/750)
- Hence, our constants are:
r = 0.15 , K = 750
- We will set up and inequality for what values of P is dP/dt > 0 and dP/dt <0
dP / dt = 0.15*P - 0.0002*P^2 < 0
= Solve for P:
P < 0 , 1-P/750 = 0 -----> P > 750
So when when P is decreasing the intervals are:
( - inf , 0 ) & ( 750 , inf )
And when P is increasing the intervals are:
( 0 , 750)
