Question

Assume the population of a country double every 20 years. The population in 2020 was 400 000. a) What will it population be in 2040? B) What will its population be in 2060? C) What will its population be in 2080?

Answer 1

A. 800 000

B. 1 600 000

C. 3 200 000

Explanation:

If you ever wondered how many people will be living in your city in the future, you can use some simple math to find out. All you need is the formula x(t) = x0 x (1 + r)^t, where x(t) is the population after time t, x0 is the initial population, r is the growth rate and t is the time in years.

For example, let's say your city had 400 000 people in 2020 and it doubles every 20 years. That means the growth rate is r = 0.0353, which you can find by solving for r when x(t) = 2x0 and t = 20.

Now you can plug in different values of t to see how many people will be living in your city in 2040, 2060 and 2080. You get:

x(20) = 400 000 x (1 + 0.0353)^20 = 800 000

x(40) = 400 000 x (1 + 0.0353)^40 = 1 600 000

x(60) = 400 000 x (1 + 0.0353)^60 = 3 200 000

Wow, that's a lot of people! You better start looking for a bigger house or a quieter neighborhood. Or maybe you can move to another city with a lower growth rate. Or maybe you can invent a time machine and go back to 2020 when things were simpler. The choice is yours!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer 2

In 2040, the population will be 800,000.

In 2060, the population will be 1,600,000.

In 2080, the population will be 3,200,000.

Explanation:

The population of a country doubles every 20 years.

The population in 2020 was 400,000.

We need to find out the population of the country in 2040, 2060, and 2080.

exponential growth formula also known as the compound interest formula

A = P(1 + r/n)^(nt)

where:

A is the final amount after time t

P is the initial principal or population

r is the annual interest rate or growth rate

n is the number of times the interest or growth is compounded per year

t is the number of years

If the population of a country doubles every 20 years, it means that the growth rate is constant at 3.5% per year (because 2^(1/20) = 1.035).

To calculate the population in future years, we can use the formula:

Population = Initial Population * (1 + Growth Rate)^(Number of Years / 20)

a) To find the population in 2040, we need to calculate the number of years from 2020 to 2040, which is 20 years. Therefore:

Population in 2040 = 400,000 * (1 + 0.035)^(20/20) = 400,000 * 2 = 800,000

b) To find the population in 2060, we need to calculate the number of years from 2020 to 2060, which is 40 years. Therefore:

Population in 2060 = 400,000 * (1 + 0.035)^(40/20) = 400,000 * 4 = 1,600,000

c) To find the population in 2080, we need to calculate the number of years from 2020 to 2080, which is 60 years. Therefore:

Population in 2080 = 400,000 * (1 + 0.035)^(60/20) = 400,000 * 8 = 3,200,000

Therefore, the population of the country in 2040 will be 800,000, in 2060 will be 1,600,000, and in 2080 will be 3,200,000, assuming a constant growth rate.

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