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Population and exponential growth

Population and exponential growth. Is it true that the world population is growing exponentially? If so, at what rate?. Identifying exponential growth. what should the "ideal" graph look like if the growth rate is indeed exponential? This graph shows growth at a 7% growth rate. y=(1.07) t

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Population and exponential growth

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  1. Population and exponential growth Is it true that the world population is growing exponentially? If so, at what rate?

  2. Identifying exponential growth • what should the "ideal" graph look like if the growth rate is indeed exponential? • This graph shows growth at a 7% growth rate. • y=(1.07)t • Just from glancing at the curve we wouldn't know that this is necessarily, exactly, exponential growth at a constant rate.

  3. Using log to identify exponential behavior • y = (1.07)t • log y = log (1.07t) = t log (1.07) • a graph of logy vs. t should be a straight line with slope of log(1.07) • Or, semi-log axes will give the same effect

  4. Growth of world population • This actually looks fairly linear! • Is it just because a relatively short period of time is observed, and the growth rate is slow? Or, is the growth non-exponential? • Source: US Census bureau http://www.census.gov/ipc/www/idb/index.php

  5. Growth of world population • The world population grew at a constant rate for many years, but in recent years, the growth rate seems to be slowing.

  6. Results and conclusions • World population is not growing exponentially at a constant rate. • One way to discuss this is to say that the rate of growth is slowing with time. • The world population growth rate was approximately 1.5% - 2% from 1950-1970 • The current growth rate is approximately 1.2% • The current rate would result in a doubling time of 70years/1.2 = 58 years. • Even so, this is a lot of people: about 76 million additional people each year. • Based on current trends and age distributions, the census bureau predicts the population growth rate will fall to 0.5% by 2050. • http://www.census.gov/ipc/www/idb/worldgrgraph.php

  7. Limitations of approach • Limitations to the data are extensively discussed on the US census bureau website. Data is a combination of census data and computer modeled projections. The largest errors are for the under-10 population. Also, in developing countries, data is less accurate (especially before the mid-1970s, there are fewer actual census data points). • Perhaps the key question for our class: As the world population grows, does that NECESSARILY mean that energy and resource use grow at the same rate? (For example, if the population doubles does that NECESSARILY mean that our petroleum use, or trash produced, or ... doubles?).

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