Out of a world population of approximately 6.6 billion, 1.2 billion people live in the richer countries of Europe, North America, Japan and Oceania and are growing at the rate of 0.25% per year, while the other 5.4 billion people live in the less developed countries and are growing at the rate of 1.5%. What will be the world population in 5 years if we assume that these rates of increase will stay constant for the next 5 years. (round answer to 3 significant digits) .

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7.03 billion.

8.03 billion.

9.03 billion.

5.03 billion.

answer is A.

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Detailed Solution

Concept- Here we will use the property that if the population of the town or country is

at present and it is increasing at a rate of

every year then the population of the town for the next year will be as below:
Population for next year Question Image

And if it continues for

years then the population of the town after

years will be equals to as below: Population after n year Question Image

Step 1: Total population of the world is given as 6.6 billion from which 1.2 billion people are richer and live in the countries of Europe, North America, Japan and Oceania and are growing at the rate of

per year.
So, after one year the population of the richer people will be equals to as below:
Question Image

represents the population of the richer people.
We can write the above expression as below by taking 1.2 common:
Question Image

After completing two years the population of the richer people will be equals to as below:
Question Image

The population after five years will be equivalent to what is listed below since this procedure lasts for five years:
The population after five years will be equivalent to what is listed below since this procedure lasts for five years.
Question Image

.
Step 2: To determine the population of those who are less wealthy, we will similarly perform step number 1, as illustrated below:
The population of those who are less wealthy will thus equal the following after one year:
Question Image

represents the population of the richer people.
We can write the above expression as below by taking 5.4 common:
Question Image

After completing two years the population of the less rich people will be equals to as below:
Question Image

The population after five years will be equivalent to what is listed below since this procedure lasts for five years:
Question Image

Step 3: The total population of the world will be equals to the addition of the richer people and less rich people as shown below:

In the equation above, we get: by inserting the values from the expressions (1) and (2) .
Question Image

By opening inside the brackets of the above equation we get:
Question Image

By opening the powers of the brackets and writing it into the multiplication form we get:

By simplifying the above equation, we get the answer as below:

Hence, option 1 is correct.

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