Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model the population of the world in the second half of the 20th century. (assume that the growth rate is proportional to the population size.) what is the relative growth rate? use the model to estimate the world population in 1992 and to predict the population in the year 2030. solution we measure the time t in years and let t = 0 in the year 1950. we measure the population p(t) in millions of people. then p(0) = 2560 and p(10) = 3040. since we are assuming that dp/dt = kp, this theorem gives the following. (round to six decimal places.)

Let the growth function that shows the population in millions after x years,

Where,

= initial population,

r = growth rate per year,

Suppose the population is estimated since 1950,

Thus, if x = 0, P = 2560,

Now, if x = 10 ( that is, on 1960 ), P = 3040,

Hence, the required function that shows the population after x years,

If x = 42,

The population in 1992  would be,

if x = 80,

The population in 2030 would be,

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen