three years ago the population of a town was 50000 .if the annual increase during three successive years was at the rate 4%,5% and 4% per annum respectively,find the present population.
Answers
Answer:
The present population is 56,784
Step-by-step explanation:
Original population of the town = 50,000
At the end of the first year,
Population = Original population + 4% of Original Population
= (1 + 4/100) * Original Population
= 1.04 * 50000
= 52000
Similarly, at the end of the second year,
Population = 52000 * 1.05 (As growth is 5%)
= 54600
Likewise, at the end of the third year,
Population = 54600 * 1.04
= 56784
In general,
If P is the original population growing at rates R1, R2, R3, ......Rn in each of the n years respectively. Then, population at the end of n years (say Pn) will be:
Pn = P*(1 + R1/100)*(1 + R2/100)*(1 + R3/100)* ........(1 + Rn/100)
(Note that R1, R2, etc are expressed in percentage)
In our case, P = 50,000, R1 = 4, R2 = 5 and R3 = 4
Final Population = 50000(1.05)(1.04)(1.05)
= 50000(1.13568)
= 56784