In the recent century, the Belgium population grows following the logistic equation. Predict its population in 2020 given the following data:
Year 1900 1950 2000
Population (mil) 6.69 8.64 10.24
One formulation of the logistic model is
P(t) = K/(1+((K-P0)/P0)e^(-rt))
So, if t is the number of years since 1900,
P(t) = K/(1+((K-6.69)/6.69)e^(-rt))
Using our two data points, taht gives us
K/(1+((K-6.69)/6.69)e^(-50r)) = 8.64
K/(1+((K-6.69)/6.69)e^(-100r)) = 10.24
Solving that for K and r, we get
P(t) = 13.0275/(1 + 0.9473e^(-0.01247t))
Now just find P(120)