This problem comes from Vaughn:
A light bulb begins to burn in the middle of outer space. It burns for one year.
a) The “sphere of light” now has a certain volume. If the light bulb keeps burning, how long must you wait for this volume to double?
b) If, after the year is up, the light bulb stops burning, how long will it take the “sphere of light” to double its volume?
For this exercise, the “sphere of light” is a rough term for the set of locations in outerspace from which an observer can see the light.
Stumble it!
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1st year – 4/3 pi light years ^3
t = time since light bulb is turned off.
1+t years – 4/3 pi (1+t)^3 light years ^3 – inner sphere near the bulb 4/3 pi t^3 light years
set twice the first year equal to the light in the 1+t years and solve.
t = -1/2 + sqrt(7/12)
approx t = .26 years.
yea verily