Question

On January 1st 2020 the populations of Japan and the Philippines were 126.5million and 109.6 respectively. Japan's population is currently decreasing by 0.2% per year while the population of the Philippines is increasing by 1.6% per year. If these rates of change remain constant, during which year will the two population be the same​

Answer 1

The populations of Japan and the Philippines will be the same in the year 2028, assuming their current growth rates remain constant.

Step-by-step explanation:

To find the year in which the populations of Japan and the Philippines will be the same, we need to set up an equation based on their population growth rates. Let's assume that the current year is 2020 and that the populations are given in millions.

The population of Japan is decreasing by 0.2% per year, which means that it is decreasing by 0.2/100 * 126.5 = 0.253 million people per year. So, the population of Japan in any year y can be represented by the equation:

P(japan) = 126.5 - 0.253y

The population of the Philippines is increasing by 1.6% per year, which means it is increasing by 1.6/100 * 109.6 = 1.7536 million people per year. So, the population of the Philippines in any year y can be represented by the equation:

P(philippines) = 109.6 + 1.7536y

To find the year when the two populations are the same, we set P(japan) = P(Philippines) and solve for y:

126.5 - 0.253y = 109.6 + 1.7536y

2.0066y = 16.9

y = 8.42

Since y represents the number of years since 2020, the two populations will be the same in the year 2020 + 8.42 = 2028.42, which can be rounded to the nearest whole number as 2028.

Answer 2

To find the year in which the populations of Japan and the Philippines will be the same, set up an equation using the population growth rates and solve for x.

Step-by-step explanation:

To find out the year in which the populations of Japan and the Philippines will be the same, we can set up an equation using the population growth rates. Let's assume the year we are looking for is 'x'.

Japan's population in year x would be: 126.5 million - (0.2% * 126.5 million) * (x - 2020).

The Philippines' population in year x would be: 109.6 million + (1.6% * 109.6 million) * (x - 2020).

Setting these two equations equal to each other, we have: 126.5 - (0.2% * 126.5) * (x - 2020) = 109.6 + (1.6% * 109.6) * (x - 2020).

Solving this equation will give us the year in which the populations will be the same.