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Chapter 1: Problem 12
What is the doubling time associated with \(3.5 \%\) annual growth?
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Using Eq. \(1.5\) and showing work, what annual growth rate, in percent, leads to the mathematically convenient factor-of-ten growth every century?
If a human body having an outward surface area of \(1 \mathrm{~m}^{2}\) continued to put out \(100 \mathrm{~W}\) of metabolic power in the form of infrared radiation in the cold of space (naked; no sun), what would the equilibrium temperature be? Would this be comfortable (put in context)?
A one-liter jar would hold about \(10^{16}\) bacteria. Based on the number of doubling times in our 24 -hour experiment, show by calculation that our setup was woefully unrealistic: that even if we started with a single bacterium, we would have far more than \(10^{16}\) bacteria after 24 hours if doubling every 10 minutes.
Verify the total solar power output of \(4 \times 10^{26} \mathrm{~W}\) based on its surface temperature of \(5,800 \mathrm{~K}\) and radius of \(7 \times 10^{8} \mathrm{~m}\), using Eq. \(1.9 .\)
In the more dramatic bacteria-jar scenario in which doubling happens every minute and reaches single-jar capacity at midnight, at what time will the colony have to cease expansion if an explorer finds three more equivalent jars in which they are allowed to expand without interruption/delay?
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