Question
The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population P, in billions of people, t years since 1975 ? (1 billion = 1,000,000,000)
- P(t) = 4(1.019)t
- P(t) = 4(1.9)t
- P(t) = 1.19t + 4
- P(t) = 1.019t + 4
The correct answer is: P(t) = 4(1.019)t
HINT – Try to make pattern by calculating population after 1 year, then 2 years and so on.
SOLUTION – It is given that Rate of growth of world’s population
= 1.9% per year
World’s population in year 1975 = 4 billion
After 1 year, population = 4 + 1.9% of 4
= 4 + 
4
= 4 ( 1 + 0.019) = 4(1.019)1
After 2 years, population = 4(1.019) + 1.9% of 4(1.019)
= 4(1.019) + (1.019)
= 4(1.019) (1 + 0.019)
= 4(1.019)(1.019) = 4(1.019)2
After t years, population = 4(1.019)t
i.e. P(t) = 4(1.019)t
So, option A is correct
We know the world's population one year after 1975 can be written as food into 1.01, nine to twelve years after 1975 can be written as '4' into 1.0 192, and so on. Similarly, suppose we continue to calculate three years after 1975. In that case, the world population will be 4.1.0 1923, and finally, we can conclude that the world population two years after 1975, as determined by the function P of t, will be equal to 4 into 1.0 19 t, and we can see that option one is the correct answer.
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