Question

The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1998.

Answer 1

Answer:

Population in 1998 year = 6.22 billion

Step-by-step explanation:

Given:-

- The population in year 1987, Po = 5 billion

- Growth rate, r = 2%

- World population follows an exponential growth model

Find:-

The projected world population in 1998.

Solution:-

- The exponential growth model is mathematically expressed as:

            Population in x year = Po* ( 1 + r/100)^( x - xo )

Where,   xo: The base year.

- Plug in the values and solve for the projected population in year 1998:

            Population in 1998 year = 5,000,000,000* ( 1 + 2/100)^( 1998 - 1987 )

            Population in 1998 year = 5,000,000,000* ( 1 + 0.02)^( 11 )

                                                     = 5,000,000,000* ( 1.02 )^( 11 )

                                                     = 6.22 billion                                

Answer 2

Answer:

The projected world population in 1998 is 6,216,871,541.95

Step-by-step explanation:

Here we have the formula for exponential growth given by

A = P(1 + r)^t

Where:

A = Population at the end of the time period

P = Population at the start of the time period

r = Rate percent of population growth

t = Time period of interest

Therefore, given r = 2% = 2/100 = 0.02, P = 5,000,000,000;

t = year 1998 - year 1987 = 11 years

We have

A = 5,000,000,000 ×$(1+0.02)^{11}$= 6,216,871,541.95

≈ 6.2 billion.