Question

As people are living longer and the world's population keeps increasing, there are more and more people ages 65 or older. Over the last 17 years, the number of people ages 65 or older has been growing exponentially, increasing about 2.7% every year. In 2017, there were approximately 656 million people ages 65 or older. If the trend continues, in what year will the population of people 65 or older surpass 1 billion?

Answer 1

To solve this problem, we can use the exponential growth formula:

Nt = N0 * (1 + r)^t

where Nt is the population at time t, N0 is the initial population, r is the annual growth rate as a decimal, and t is the number of years.

We know that N0 = 656 million, r = 0.027 (since the population is growing at a rate of 2.7% per year), and we want to find the year when Nt = 1 billion.

Substituting in these values, we get:

1 billion = 656 million * (1 + 0.027)^t

Simplifying:

1.524 = 1.027^t

Taking the natural log of both sides:

ln(1.524) = t * ln(1.027)

Dividing by ln(1.027):

t = ln(1.524) / ln(1.027)

Using a calculator:

t ≈ 23.1 years

Therefore, if the trend continues, the population of people ages 65 or older will surpass 1 billion in approximately 23.1 years from 2017.

Answer: 2040 (rounded to the nearest whole year).