Exponential Modeling
1. The population of the Russia in 1998 was 147 million; the population of Nigeria was 106 million. Russia is decreasing in population by approximately 0.1% annually; the population of Nigeria is growing at 3%. Using Excel, predict the year when Nigeria's population will exceed Russia's, assuming that the current trend continues. How much faith do you have in your answer? What factors could affect the validity of your prediction?
Nigeria's population would exceed Russia's in 2009. One should be a little bit skeptical about the prediction because it is difficult to maintain a rate of 3% for a long period of time. On the other hand, it is only ten years, so it is not completely unreasonable. In fact Nigeria's populaton first exceeded Russia's population in 2006, so the prediction was quite good. By the way the growth rate of Nigeria did come down from 3%. In 2025, the growth rate was 2.4% for example.
2. World oil production was 518 million tons in 1950. Between 1950 and 1972, production increased at a rate of 7% per year. World oil production in 1998 was approximately 3300 million tons.
a. Using the information above, estimate the world oil production in 1972.
518⋅(1.07)^22 ≈2295 million tons.
b. Using the result of part a, determine how much oil would have been produced in 1998 if growth in production had continued at a rate of 7% between 1972 and 1998. Compare this result to the actual 1998 figure given above.
518⋅(1.07)^48 ≈13328 million tons. This number is over 4 times the actual amount.
c. Using the result of part a, determine how much oil would have been produced in 1998 if growth in production had proceeded at a rate of 3% between 1972 and 1998. Compare this result to the actual 1998 figure given above.
2295⋅(1.03)^26 ≈4949 million tons. This number is above the actual, but it is closer.
d. Using your answer from part a, estimate the actual average annual growth rate in world oil production between 1972 and 1998.
Based on the answer in c, it would definitely be less the 3%. A reasonable guess might be 2%, but the actual average rate is 1.41%.