Respuesta :
Answer:
dP/dt = 0.047P
Step-by-step explanation:
- Let P(t) be the number of insects at time t.
- Let the birth rate for the insects be b(t, P) , then b(t, P) = 6.7% = 0.067
- Let the death rate for the insects be d(t, P) , the d(t, P) = 2% = 0.02
The number of insects between time t and t + Δt is given as
Total birth = bPΔt
Total death = dPΔt
The rate of change of population with respect to time is
ΔP = bPΔt - dPΔt
ΔP = (b - d)PΔt
ΔP/Δt = (b - d)P
Taking the limit as ΔP approaches 0
dP/dt = (b - d)P
Using the values of b and d, we have
dP/dt = (0.067 - 0.02)P = 0.047
dP/dt = 0.047P
The rate of change should be dP/dt = 0.047P
Calculation of the rate of change:
Since we assuming the following things:
P(t) be the number of insects at time t.
The birth rate for the insects be b(t, P) , so b(t, P) = 6.7% = 0.067
And, the death rate for the insects be d(t, P) , the d(t, P) = 2% = 0.02
Now
The number of insects between time t and t + Δt should be provided
Total birth = bPΔt
Total death = dPΔt
Now The rate of change should be
ΔP = bPΔt - dPΔt
ΔP = (b - d)PΔt
ΔP/Δt = (b - d)P
Now we considered the limit as ΔP approaches 0
So,
dP/dt = (b - d)P
Now
dP/dt = (0.067 - 0.02)P = 0.047
dP/dt = 0.047P
hence, The rate of change should be dP/dt = 0.047P
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