Final answer:
The population of the village after 2 years, growing at an annual rate of 10%, will be 36,300.
Step-by-step explanation:
The present population of a village is 30,000 and it is increasing at a rate of 10% per annum. To find out the population after 2 years, we can use the formula for compound growth which is:
P(t) = P0 (1 + r)^t
where:
- P(t) is the future population
- P0 is the present population
- r is the annual growth rate in decimal form
- t is the number of years
Substituting the given values:
- Convert the percentage rate to decimal by dividing by 100: r = 10% / 100 = 0.10
- Place the values into the formula: P(2) = 30,000 (1 + 0.10)^2
- Calculate the growth for each year: P(2) = 30,000 (1.10)^2
- Solve the exponent: P(2) = 30,000 x 1.21
- Find the future population: P(2) = 36,300
Therefore, the population of the village after 2 years will be 36,300.