Schick razor intuition full#

How many rabbits are there at the start of the third year? So the second year starts with 320 rabbits. Thus after the first year our starting population of 20 rabbits has doubled 4 times, from 20 to 40, then to 80, then to 160, then to 320. Now the doubling time for populations of rabbits under ideal conditions is about 3 months, or 1 season, so they double their number 4 times per year. Suppose for the sake of the example that this is a large meadow that continuously produces enough food and water and contains enough space to support a thousand rabbits. There is no such thing as an infinite meadow: every meadow produces just so much food and water, and has just so much space. Suppose we start with 10 breeding pairs of bunnies living in a fenced meadow. Three times 7 is 21, so when we check the jug 24 hours before it overflows it is less than one-eighth full-mostly empty. * So 7 hours before the jug overflows it is half full, and 7 hours before that it is one-quarter full, and 7 hours before that it is one-eighth full. For the fungus to fill a gallon jug in 4 days starting from just a pinch means it has to double about once very 7 hours or so. In natural growth the time it takes for whatever is growing to double in size is always the same regardless of how big or small it is. One way of understanding how this could be so is to think in terms of doubling times. But in fact the jug is still mostly empty the day before.

Schick razor intuition full#

If natural growth matched our intuition, the jug would be three-quarters full the day before it overflows. This is why so many rates of growth, such as the growth of an investment or the growth of a population, are expressed in percentages-per-unit-time. In most kinds of natural growth it is not a fixed amount but a proportional amount that is added at regular intervals. But most natural growth is nothing like that. Growth, we think, means adding a fixed amount for each fixed period of time. Our lives grow with the steady accumulation of the years themselves. Trees grow a few feet each year just as children grow by 5 to 7 pounds each year. I find that if the lecture isn’t provocative students are unlikely to absorb the main point, because people tend to think of growth as something steady.

This question is one I pose to students in general math courses at the start of my standard lecture on modeling natural growth, a lecture with the deliberately provocative title of this chapter. How full was the jug the morning of the 3rd day? Suppose you do this one morning, and that exactly 4 days later you find that the fungus has filled the jar and is just beginning to overflow it. Take a pinch of the spores of a certain fungus and drop them into a gallon jug, one whose walls are coated with nutrient so the fungus can grow as fast as it likes.