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Which would you choose??
Our writing exercise involves using semi-log graph paper.
Modification... only graph your balance every other year!
Linear scale: numbers are evenly spaced.
Logarithmic scale: powers of 10 are evenly spaced.
When a quantity grows...
exponential growth | linear growth |
---|---|
$$P(t)=P_0e^{kt}$$
'J'-curve on regular plot straight line on semi-log plot Has a constant doubling time or half-life |
$$y(t)=b+m*t$$
straight line on regular plot flattening-out curve on semi-log plot Has a constant slope or rate-of-change |
Jill was offered a weekly wage starting at $10 and doubling every 2 weeks.
Molly is offered a weekly wage of 10 cents, but it will triple every 2 weeks.
Moore's "Law" is the observation that the number of transistors in the Central Processing Units (CPUs) of computers has been doubling approximately every two years since ~1970. Note the semi-log y-axis:
Bacteria grow by dividing. So each successive generation will have twice as many 'children' as the previous generation.
The number of lily pads on a pond doubles every 5 days.
Counting backwards from the time at which the pond is fully covered (100%), how many days before was 1/4 of the pond covered with lily pads?
Here is a similar graph for the population of humans on Earth...
What's the human population "doubling time"?
Semi-log plot, by region (from U.N. data):
New technologies typically "take off" (grow exponentially) for a while before market saturation kicks in (everyone's got one).
Renewable resources follow the same shape for consumption vs time: An S-curve or logistic curve.
U.S. Hydroelectric capacity (USGS)
More recently...Wikipedia graph of EIA data. [What do you think accounts for all that recent variation?]
Resources that are not being replenished do not have a long-term "plateau" at which they can be eternally exploited.
What have you heard about "peak oil"? What is that?
More recently...EIA data 1860-present.
For comparison a large coal power plant might have a capacity of 1500 MW, and the Three Gorges Dam plans on 22,500 MW.