Question

This exercise uses the population growth model. The population of the world was 5.7 billion in 1995 and the observed relative growth rate was 2% per year. By what year will the population have tripled?

Answer 1

Using the exponential growth formula, the world population of 5.7 billion in 1995 is expected to triple by around the year 2049, given a growth rate of 2% per year.

Step-by-step explanation:

To determine by what year the world population, which was 5.7 billion in 1995, will have tripled given a relative growth rate of 2% per year, we can use the formula for exponential growth: P(t) = P0 * e^(rt), where P(t) is the future population, P0 is the initial population, r is the growth rate, and t is the time in years.

First, we calculate the future population needed for a triple increase: 5.7 billion * 3 = 17.1 billion. Then, we set up the equation: 17.1 = 5.7 * e^(0.02t). Solving for t gives us the time in years it will take for the population to triple:

17.1 / 5.7 = e^(0.02t)

3 = e^(0.02t)

Taking the natural logarithm of both sides of the equation, we get:

ln(3) = 0.02t

Finally, we solve for t:

t = ln(3) / 0.02 ≈ 54.88 years

Adding this to the year 1995, we determine that the world population is expected to triple by around the year 2049.