Question

The population of a village increases at the rate of 7% every year. If the present population is 90,000, what will be the population after 2 years?

Answer 1

To find the population after 2 years with a 7% annual growth rate, the exponential growth formula P(t) = P0 * (1 + r)^t is used. With an initial population of 90,000, the population after 2 years is calculated to be approximately 103,041.

Step-by-step explanation:

To calculate the population of a village after 2 years with a 7% annual growth rate, we will use the formula for exponential growth:

P(t) = P0 * (1 + r)^t, where:
- P(t) is the population after t years
- P0 is the initial population
- r is the growth rate
- t is the number of years

Given that the present population (P0) is 90,000 and the growth rate (r) is 7% or 0.07, we need to find P(t) for t = 2.

Here is the step-by-step calculation:

1. Convert the percentage growth rate to its decimal form: 7% = 0.07.
2. Calculate the population after 1 year: P(1) = 90,000 * (1 + 0.07)^1 = 90,000 * 1.07 = 96,300.
3. Calculate the population after 2 years: P(2) = 90,000 * (1 + 0.07)^2 = 90,000 * 1.07^2 = 90,000 * 1.1449 ≈ 103,041.

Therefore, the population of the village after 2 years will be approximately 103,041.