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Solving for Time and Rates

Now for some population stuff:

The world's population in 1950 was 2,555,982,611.  In 1970, it was 3,706,601,448.   Find the rate of growth.

* Remember our population equation:

P = P not * e^( rt )

Set it up:

3706601448 = 2555982611e^( r( 20 ) ) ... 3706601448 / 2555982611 = e^( 20r ) ... clear the path! ... Ln( 3706601448 / 2555982611 ) = Ln * e^( 20r ) ... kill the e! ... Ln( 3706601448 / 2555982611 ) = 20r ... almost done! ... Ln( 3706601448 / 2555982611 ) / 20 = r ... r = approximately .0185839 ... Don't round too much here or you won't be as accurate in this next part!

What about predicting?

Can you predict what the world's population will be in 2050?

      Let's use the 1950 figure for ourP not:

P not = 2,555,982,611

       And we can use the growth rate we just found:

r = approximately .0185839

       1950 to 2050 gives us t = 100...

P = 2555982611 * e^( .0185839 ( 100 ) )

Grab a calculator!

P = approximately 16,392,546,229

So, we predict that there will be 16,392,546,229 people on earth in 2050.