Verified answer

This is actually a problem of geometric progression.

So, population in 2000 = 1.013 * 6 billion (1.013 = 1.3 % growth)

Population in 2001 = 1.013 * population of 2000 = 1.013 * 1.013 * 6 billion = 1.013 raised to 2 * 6 billion

and so on...

So, in 2008, population will be

(1.013 raised to (2008 - 1999)) * 6 billion = 1.123 * 6 = 6.739 billion

In 2020 (1.013 raised to 21) * 6 billion = 1.311 * 6 = 7.869 billion

Let's assume n = year, therefore f(n) = world's population

So f(n) = (1.013 raised to (n - 1999)) * 6 billion

Let 1999 be year zero (ie our reference year)

Population in 1999 = 6.0 x 10^9

Now 1.3% = 0.013 so the increase each year is 0.013

This means that the population the following year = population of preceding year x 1.013

So Population in 2000 (ie year 1) = 6.0 x 10^9 x 1.013

Population in 2001 (ie year 2) = 6.0 x 10^9 x 1.013 x 1.013

more simply

Population in 2001 = 6.0 x 10^9 x (1.013)^2

Population in 2002 (ie year 3) = 6.0 x 10^9 x (1.013)^2 x 1.013

ie Population in 2002 = 6.0 x 10^9 (1.013)^3

So the pattern that is emerging is that the population in year n is

6.0 x 10^9 (1.013)^n where n = year - 1999

Now let P(n) = the population in year n

So the required function is P(n) = 6.0 x 10^9 (1.013)^n

where n = year - 1999

OK so in the year 2020, n = 2020 - 1999 ie n = 21

So P(21) = 6.0 x 10^9 (1.013)^ 21

= 7.9 x 10^9 (rounded to 2 significant figures) and this is the estimated population in 2020

1999: 6,000,000,000

2000: 6,000,000,000 + 6,000,000,000 x 0.013 = 6078000000

2001: 6078000000 + 6078000000 x 0.013 = 6157014000

2002: 6157014000 + 6157014000 x 0.013 = 6237055182

keep following this pattern until you get to the year 2008, and then continue on to the year 2020

you should find the population in 2008 is 6,739,633,163

and the population in 2020 is 7,869,544,634

The equation would be:

Population in year X = 6,000,000.000 x (1 + 0.013)^(X-1999)

In case you don't understand the symbol ^ in the equation, it represents the power. You might read the equation as

"The population in year X equals the sum of one plus zero point zero one three, all to the power of the difference of X minus 1999, times six billion"

In 2008, the world population would be 624000000.

In 2020,the world population would be 1560000000

To write the function,

Let"X" be the population of world at any time.

X=6000000000 * 1.3/100 * the number of years after 2000 that you have to calculate.

Hope this is correct.