Question

The population of the world in 2010 was 25 billion and the relative growth rate was estimated at 0.25 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2018.

Answer 1

Let the equation for the population (P) growth be given by

where is the initial population in billions at time 2010 = 25

t is the number of years since 2010 to 2018

t=2018-201=8

r is the rate of growth of population/year = 0.25

, hence the population would be 184.73 billion in 2018

Answer 2

To find the projected world population in 2018 using an exponential growth model, we can use the formula:

P(t) = P0 * e^(r * t)

Where: P(t) is the population at time t P0 is the initial population e is the base of the natural logarithm (approximately 2.71828) r is the relative growth rate (expressed as a decimal) t is the time interval

Given: P0 = 25 billion r = 0.25% per year = 0.0025 (as a decimal) t = 2018 - 2010 = 8 years

Plugging the values into the formula:

P(2018) = 25 billion * e^(0.0025 * 8)

Using a calculator, we can evaluate the expression:

P(2018) ≈ 25 billion * e^(0.02) P(2018) ≈ 25 billion * 1.02020134082

P(2018) ≈ 25 billion * 1.5200345055 P(2018) ≈ 38 billion

Therefore, the projected world population in 2018, based on the given assumptions and an exponential growth model, is approximately 38 billion.