Question

If a country's population in 1995 was 184 million, in 2002, it was 188 million. What is the population in 2006 using the exponential growth formula? Round your answer to the nearest million.

a. Not enough information provided.
b. 190 million.
c. 192 million.
d. 194 million.

Answer 1

To estimate the population in 2006 using the exponential growth model, one must first calculate the annual growth rate using the given population data from 1995 and 2002, then apply this rate to estimate the population for 2006 and round to the nearest million.

Step-by-step explanation:

To solve for the population in 2006 using the exponential growth formula, we need to first determine the annual growth rate between 1995 and 2002. Since the population grew from 184 million to 188 million in 7 years, we can use the formula:

P = P0ert

Where P is the final population, P0 is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is the time in years. Rearranging the formula to solve for r, we have:

r = (1/t)ln(P/P0)

Substituting the values, we have:

r = (1/7)ln(188/184)

Once we find r, we can then calculate the population for 2006, which is 4 years after 2002, using the formula:

P = 188er(4)

After calculating r and then using it to find P for 2006, you would round the result to the nearest million to find the answer to the given multiple-choice options.