Gardening, math: exponential growth
Self-tutoring about gardening: the tutor thinks about the growth rate of a pumpkin.
The following is by my understanding.
The pumpkin plants in the backyard have finally managed a couple of pumpkins, each about one inch in diameter.
To my mind, it’s quite late in the season for a pumpkin fruit to start developing. Suppose it needs to be eight inches in diameter, for instance, and that it’s got two months left to grow. (Since Halloween is Oct 31, that might make sense.)
If the pumpkin needs to multiply its diameter by eight times in around sixty days, what growth rate is needed? Well, growth means increase in mass, which is directly proportional to volume. Since, for a sphere, V≈1.3333πr3, multiplying the diameter by eight (which also means multiplying the radius by eight) means multiplying the volume by 83 or 512.
Next, we have the rule of 72 for exponential growth, which states that the doubling time multiplied by the growth rate roughly equals 72.
To multiply itself by 512, the pumpkin must double in size nine times: 29=512. Imagining 63 days, that means it needs to double every seven days. By the rule of 72, that means the pumpkin needs to grow by about ten percent each day.
That growth rate might seem optimistic, but I doubt it’s impossible: when a plant is determined, it can do amazing things.
I guess we’ll see:)
Source:
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.