When will the world’s population reach 7 billion?

Let’s look at a similar problem we did (for homework recently)

Salma puts $1 000 into the bank. The bank pays 10% interest per year.

How long is it before Salma has $1 500 in her account?

We plotted a graph of how Salma’s money grew over time.

And in order to plot the graph, we needed points (from some simple calculations)

After 1 full year, she has $1000 x 1.1 or $1100

After 2 full years, she has $1000 x (1.1)2 or $1210

After 3 full years, she has $1000 x (1.1)3 or $1331 and so on …

So the table of values we need to draw the graph looks like this:

Time (in full years) Amount of money ($)

0 1000

1 1100

2 1210

3 1331

4 1464.10

5 1610.51

6 1771.56

And here’s the graph (in geogebra)….

The red curve shows the growth of the money in the account

We now need to find when the y-coordinate reaches 1500 (hence the blue line)

And here’s the answer …

Geogebra will give the coordinates of the point of intersection (point A on the diagram)

The answer is – Salma will have $1500 after 4.254 years.

An algebraic way of solving the problemThe growth of Salma’s money is described by the equation:

A = 1000 x (1.1)t

And we simply want to solve the equation 1500 = 1000 x (1.1)t

This simplifies to 1.5 = (1.1)t

Taking logs of both sides …

log10 1.5 = log10 1.1t

⇒ t = log10 1.5 log10 1.1

⇒ t = 4.254 years

⇒ log10 1.5 = tlog10 1.1 (using one of our rules of logs)

So … back to the world population problem …

To some degree the population is growing like Salma’s money

Some questions …

What’s the starting population?

What is the percentage increase per year of the population?

This will help …

http://www.worldometers.info/population/

Or this ….