Answer:
a)
If we call P(n) the population n years after 2010, the recurrence relation for the population of the world n years after 2010 would be
P(0) = 6.9 billion
P(n) = P(n-1)*(1.011)
b)
[tex]P(n)={6.9*(1.011)^n[/tex]
c)
[tex]6.9*(1.011)^{20} = 8.5876\; billion[/tex]
Step-by-step explanation:
a)
If the growing rate is 1.1% in the year 2011 was
6.9 + 1.1% of 6.9 = 6.9 + 6.9*(0.011) = 6.9*(1.011)
In the year 2012, the new population was
6.9*(1.011) + 1.1% of 6.9*(1.011)
= 6.9*(1.011) + 6.9*(1.011)*(0.011) = 6.9*(1.011)*(1+0.011)
= 6.9*(1.011)*(1.011) = [tex]6.9*(1.011)^2[/tex]
Similarly, we can see that the population in 2013 was
[tex]6.9*(1.011)^3[/tex]
If we call P(n) the population n years after 2010, the recurrence relation for the population of theworld n years after 2010 would be
P(0) = 6.9 billion
P(n) = P(n-1)*(1.011)
b)
In the year n after 2010, the population would be
[tex]P(n)={6.9*(1.011)^n[/tex]
c)
The population of the world in 2030, according to the formula, will be P(20)
[tex]\boxed{P(20) = 6.9*(1.011)^{20} = 8.5876\; billion}[/tex]
