Answer:
a)55.48 years
b)9.725 billions
Step-by-step explanation:
First of all, note that when you increase certain amount by x percent, you only have to multiply that amount for a decimal number following this rule:

For example, if you increase 5.3 billion by 20%, then:


In the problem you need to increase the population by 2%/year, then after one year you'll have:

Note that this last quantity will increase 2% in the second year, then:

In the third year the population will be:

Then, the function Q(t) that expresses the world population (in billions) is given by:

where t=0 corresponds to the beginning of 1990 (5.3 billions).
a)The time necessary for the population to triple in size is given by:

To solve for t, you need to apply the natural logarithm or the common logarithm in both sides of the equation:
![ln(3)=ln[(1.02)^{t}]\\ln(3)=t(ln(1.02))\\t=\frac{ln(3)}{ln(1.02)}\\ t=55.48 years](https://tex.z-dn.net/?f=ln%283%29%3Dln%5B%281.02%29%5E%7Bt%7D%5D%5C%5Cln%283%29%3Dt%28ln%281.02%29%29%5C%5Ct%3D%5Cfrac%7Bln%283%29%7D%7Bln%281.02%29%7D%5C%5C%20t%3D55.48%20years)
Then, the time required to the population to triple in size is 55.48 years.
b)If the growth rate were reduced to 1.1%/year, the function would be:

The world population at the time obtained in a) would be:
