Originally Posted by

**nick61416** Year: 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Pop: 2555 2780 3040 3346 3708 4087 4454 4850 5276 5686 6079

I have this data and i'm asked

(a) Assuming that the above equation holds, use the data from 1950 through 1970 to estimate .

(b) Use the fourth-order Runge-Kutta method, using the value of determined above, to simulate the world population from 1950 to 2050 with a step size of 5 years. Display your simulation results along with the data on the plot.

HINT:

Introduce the incremental year, dx, starting from x=1950 by

dx = x – 1950

so that dx for x=1950 is 0 and dx=20 for x=20 and so on.

Use the world population for dx0=0, 5, 10, 15 and 20 to interpolate p by the Lagrange polynomial.

The derivative of the polynomial is given by another polynomial

>> DC=polyder(C);

which is evaluated at dx0 to give

>> dp0=polyval(DC, dx0);

i am really struggling with this right now any help would be great

thanks