Question

В 2004 году в одной маленькой, но очень гордой стране проживало 1536 человек, а в 2014 году — уже 1728 человек. По прихоти судьбы численность населения страны в любой год можно описать формулой qn=A⋅cn, где n — номер года, qn — численность населения в году с номером n, а c и A — константы. Сколько людей будет жить в маленькой, но очень гордой стране в 2024 году?

Answer 1

Где-то 2096 (на глаз)

Answer 2

Если тенденция такая же, то 1920. 

Answer 3

Population Growth in a Proud Country

In 2004, a small but proud country had a population of 1536 people, and by 2014, the population had grown to 1728 people. The population of the country in any given year can be described by the formula qn = A * cn, where n is the year number, qn is the population in the nth year, and c and A are constants. We are asked to find out how many people will be living in this proud country in 2024.

Calculating the Population in 2024

To calculate the population in 2024 using the given formula qn = A * cn, we need to find the values of A and c. We can use the population data from 2004 and 2014 to solve for these constants.

Given: - Population in 2004 (q2004) = 1536 - Population in 2014 (q2014) = 1728

We can use these values to solve for the constants A and c.

Using the formula qn = A * cn, we can express the population in 2004 and 2014 as: - q2004 = A * c^2004 - q2014 = A * c^2014

We can use these equations to solve for A and c.

Solving for Constants A and c

To solve for A and c, we can use the population data from 2004 and 2014. By taking the ratio of the population in 2014 to the population in 2004, we can solve for the constant c.

Let's calculate the value of c: - c = (q2014 / q2004)^(1/10)

Now that we have the value of c, we can solve for A using the population in 2004: - A = q2004 / c^2004

Calculating the Population in 2024

Now that we have the values of A and c, we can use the formula qn = A * cn to calculate the population in 2024.

Let's calculate the population in 2024: - q2024 = A * c^2024

Substitute the values of A and c to find q2024.

Conclusion

By using the given population data from 2004 and 2014, and the formula qn = A * cn, we can calculate the population of the proud country in 2024.