How Long Until Superman Regains His Powers?

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SUMMARY

The discussion focuses on calculating the time it takes for Superman to regain his powers after being affected by kryptonite, which decays exponentially. Using the decay constant r = -0.138629, the equation Q(t) = Qe^(rt) is applied to determine when 90% of the kryptonite has disintegrated. The correct calculation leads to a time of approximately 16.6 days before Superman can regain his powers, confirming that the answer is closest to option d, 17 days.

PREREQUISITES
  • Understanding of exponential decay and decay constants
  • Familiarity with natural logarithms and their properties
  • Ability to manipulate exponential equations
  • Basic knowledge of the context of kryptonite in Superman lore
NEXT STEPS
  • Study exponential decay functions in mathematical modeling
  • Learn about the applications of natural logarithms in real-world scenarios
  • Explore more complex decay problems in physics and chemistry
  • Investigate the implications of kryptonite on Superman's abilities in various comic storylines
USEFUL FOR

This discussion is beneficial for physics students, comic book enthusiasts, and anyone interested in mathematical modeling of decay processes.

Yohan Lee
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Homework Statement


superman has been disabled by a nearby amount of kryptonite, which decays exponentially. If Superman cannot regain his power until 90% og the kryptonite disintegrates, then how long will it be before he regain his powers?
Use r=-0.138629. Round to the nearest day.
a. 4days c 11days
b 6days d 17days e 21days

Homework Equations


Q(t) = Qe^(rt)

The Attempt at a Solution


i tried 0.9Q=Qe^(-0.138629t)
0.9=e^(-0.138629t)
ln0.9=lne^(-0.138629t)
ln0.9=-0.138629t
ln0.9/-0.138629 =t
t=0.760018
and i was not able to find the answer
 
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If 90% has decayed, how much is left?
 
Thank you i got 0.1Q=Qe^(-0.138629t)
t= 16.6