In a particular small town, the population in 1995 was 1200. Ever since then the population has grown by 4% every year. If conditions stay the same, what is the approximate expected population in the year 2000?
To calculate the approximate expected population in the year 2000, we need to determine the population growth rate for each year and then apply it to the initial population.
Here's how we can do it step by step:
1. Calculate the growth rate per year: 4% growth means the population increases by 4% of its previous value each year.
2. Determine the total number of years between 1995 and 2000, which is 5 years.
3. Apply the growth rate for each year: Multiply the population by (1 + growth rate) for each year.
4. Calculate the approximate expected population in the year 2000 by adding the growth to the initial population.
Let's calculate it:
1. Calculate the growth rate per year:
Growth rate = 4% = 0.04 (as a decimal)
2. Determine the total number of years between 1995 and 2000:
Total years = 2000 - 1995 = 5 years
3. Apply the growth rate for each year:
Population in 1995: 1200
Year 1 (1996): Population = 1200 * (1 + 0.04) = 1200 * 1.04 = 1248
Year 2 (1997): Population = 1248 * (1 + 0.04) = 1248 * 1.04 = 1297.92
Year 3 (1998): Population = 1297.92 * (1 + 0.04) = 1297.92 * 1.04 = 1349.61
Year 4 (1999): Population = 1349.61 * (1 + 0.04) = 1349.61 * 1.04 = 1403.07
Year 5 (2000): Population = 1403.07 * (1 + 0.04) = 1403.07 * 1.04 = 1458.22
4. Calculate the approximate expected population in the year 2000:
The approximate expected population in the year 2000 is 1458.22.
Therefore, the population in the year 2000, given a 4% growth rate, is approximately 1458.