Final answer:
Using the exponential growth formula, we calculated an annual growth rate based on the population data from 1995 and 1999. Using this rate, we estimated the population in 2009 to be approximately 117 million when rounded to the nearest million.
Step-by-step explanation:
To estimate the population in 2009 using the exponential growth formula, we need to know the initial population, the growth rate, and the period over which the population is growing. From the data provided, we have an initial population of 98 million in 1995 and a population of 103 million in 1999. Let's calculate the approximate annual growth rate first.
The formula for exponential growth is:
P(t) = P0 * e^(rt)
where:
- P(t) is the population at time t,
- P0 is the initial population,
- r is the growth rate,
- t is the time in years,
- e is the base of the natural logarithm.
First, we need to find r, the growth rate, using the population values from 1995 and 1999:
103 = 98 * e^(4r)
Solving for r:
1.05102041 = e^(4r)
r ≈ ln(1.05102041) / 4 = 0.0125 or 1.25% per year
Now, using this growth rate, we can estimate the population in 2009:
t = 2009 - 1995 = 14 years
P(2009) = 98 * e^(0.0125 * 14)
P(2009) ≈ 98 * e^(0.175) ≈ 98 * 1.19175 ≈ 116.7915 million
Rounded to the nearest million, the estimated population in 2009 is 117 million.