Question

A small country had a population of 2,254,000 people in the year 2000. If the population declines steadily at a rate of 3.5% each year, what is the expected population of this country in the year 2015? Write an equation.

Answer 1

The expected population of the country in 2015 can be calculated using the exponential decay formula: Population in 2015 = 2,254,000 × (1 - 0.035)^15. This equation accounts for a 3.5% yearly decline over 15 years from the year 2000.

Step-by-step explanation:

To calculate the expected population of a country in the year 2015 based on a steady decline rate, we can use an exponential decay formula. If the population in the year 2000 was 2,254,000 people and it declines at a rate of 3.5% per year, the population in the year 2015 will be calculated as:

Population in 2015 = Initial population × (1 - decay rate)number of years

Let's convert the percentage decay rate to decimal form (3.5% = 0.035) and calculate:

Population in 2015 = 2,254,000 × (1 - 0.035)2015 - 2000

Population in 2015 = 2,254,000 × (0.965)15

By solving this equation using a calculator, the expected population for the year 2015 can be found.