The world's population was 5.51 billion on January 1, 1993 and 5.88 billion on January 1, 1998. Assume that at any time the population grows at a rate proportional to the population at that time. In what year should the world's population reach 7 billion? (Give a calendar year. For example: 2001)

As the population grows at a ate proportional to the population at that time, we can determinate the linear relationship between the time and the world's population.

We have two point:

January 1, 1993 (x1=0) ⇒ world's population was 5.51 billion (y1= 5.51)

January 1, 1998 (x2=5) ⇒ world's population was 5.88 billion (y2= 5.88)

The linear relationship between this two variables can be represent by the equation:

y=a*x+b (linear function)

a ⇒ slope

b ⇒ intercept with y-axes

a=[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{5.88-5.51}{5-0}=\frac{0.37}{5}=0.074[/tex]

b=y-a*x

Using (x1,y1)

b=5.51-0.074*0=5.51

y=0.074*x+5.51

Now we can estimate how many years from 1991 the population will be 7 billion

y3=7

x3= ?

(y3-5.51)/0.074= x3

(7-5.51)/0.074=x3

20.135=x3

The result is not an exact value, but this decimal value will represent a few extra days after January 1, 2011 (20 years after January 1, 1991), but as the question as for a calendar year and not and exact day we will just work with the 20 years

We can say that in 2011 the world's population will be 7 billions