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)

Answer:In 2011 the world's population will be 7 billionsStep-by-step explanation:Lets choose January 1, 1993 as 0 time, so January 1, 1998 is time 5, because is 5 year after.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 ⇒ slopeb ⇒ intercept with y-axesa=[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*xUsing (x1,y1)b=5.51-0.074*0=5.51y=0.074*x+5.51Now we can estimate how many years from 1991 the population will be 7 billiony3=7x3= ?(y3-5.51)/0.074= x3(7-5.51)/0.074=x320.135=x3The 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 yearsWe can say that in 2011 the world's population will be 7 billions