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 1991.
1991 is 4 years from 1987, so the projection is (in billions)
5 * 1.02^4
To find the projected world population in 1991, you can use the exponential growth model formula:
P(t) = P0 * e^(rt)
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 growth rate
t is the time interval
In this case, the initial population in 1987 (P0) is 5 billion, the growth rate (r) is 2% or 0.02, and the time interval (t) is 1991 - 1987 = 4 years.
Now, let's plug in these values into the formula:
P(t) = 5 billion * e^(0.02 * 4)
To calculate the exponent, multiply the growth rate (0.02) by the time interval (4):
P(t) = 5 billion * e^(0.08)
Next, calculate the value of e^(0.08) using a calculator. It equals approximately 1.08328707:
P(t) = 5 billion * 1.08328707
Now, multiply the population in 1987 (5 billion) by the result:
P(t) = 5 billion * 1.08328707 = 5.41643535 billion
Therefore, the projected world population in 1991 would be approximately 5.42 billion.