Consider bacterial growth by cell division, in which one bacterium becomes two, the two divide to become four, the four divide to become eight, and so on. Steady growth in a finite environment gets interesting. If you wait until your money in the bank doubles due to an interest rate of 2% per year, get ready for a 35-year wait. A city planning commission that accepts what seems like a modest 3.5% annual growth rate may not realize that this means that doubling will occur in 20 years that’s a need for double capacity for such things as water supply, sewage-treatment plants, and other municipal services every 20 years. Space for any growing population must be planned. For example, if Bozeman, Montana, maintains an annual growth rate of 4%, its population will double every 17.5 years (70/4 = 17.5 years). There is an important relationship between the percent growth rate and its doubling time known as “the rule of 70”: to estimate the doubling time for a steadily growing quantity, simply divide the number 70 by the percentage growth rate. For example, if the population of a growing city takes 10 years to double from 100,000 to 200,000 inhabitants and its growth remains exponential, then in the next 10 years the population will double to 400,000 and 10 years after that to 800,000 and so on. The importance of the exponential curve of Figure 1 is that the time required for the growing quantity to double in size, a 100% increase, is a constant. When the growth of a quantity is exponential, the amount doubles in a certain interval of time. This doubling of quantity becomes startling when you find the car you financed to purchase costs nearly twice as much as if you paid cash. Notice that each of the successive equal time intervals on the horizontal scale corresponds to a doubling of the quantity on the vertical scale. The curve in Figure 1 depicts exponential growth for any of the above examples. Much of the growth in the world around us is exponential. For example, investment accounts may grow at 2% per year the population of a region may grow at 3% per year, and electric power generating capacity in the United States may grow at about 7% per year (as occurred during the first three-quarters of the twentieth century). When a quantity such as money in the bank, population, or the consumption rate of a resource grows steadily, at a fixed percentage per year, we say the growth is exponential. Let’s be careful of what we wish for-especially if growth is exponential. A global pandemic challenges this notion. In general, growth is seen as a good thing. How often do we hear the adage, “Growth is good?” An economy that grows is good.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |