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Q: What is the equation to solve half life problems?
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The half-life is the time it takes for half of the sample to decay. The formula to use is N(t) = N(0) / 2^(t/half life), where N(0) is what we have at the start, and N(t) what is left at time t.


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How would the half life equation of aluminum be balanced differently?

Not exactly sure what you mean about "aluminum's half life equation." Exponential decay, from where we get the half-life equation from, has nothing to do with mass, atomic number, etc... and therefore has nothing to do with any particular isotope.


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How can you use logarithmic and exponential equations and properties to solve half-life and logistic growth scenarios?

For an exponential function: General equation of exponential decay is A(t)=A0e^-at The definition of a half-life is A(t)/A0=0.5, therefore: 0.5 = e^-at ln(0.5)=-at t= -ln(0.5)/a For exponential growth: A(t)=A0e^at Find out an expression to relate A(t) and A0 and you solve as above


Is an isotope still radioactive after a half life?

Yes, an isotope is still radioactive after one half life. There is simple one half of it left. And there will be one half of that half, i.e. one quarter left after a second half life, and half of that half, i.e. one eight left after a third half life, etc. The equation for half-life is ... AT = A0 2(-T/H) ... where A0 is the starting activity, AT is the ending activity at some time T, and H is the half-life in units of T. Sometimes, you see this equation in other forms, such as with e instead of 2, but there is another factor in the exponent. They are all the same. This equation, with the 2, makes the meaning of half-life clear because a negative power of 2 is simply 1/2, 1/4, 1/8, etc.


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What does the 1 over 2 in a half life equation represent?

A half life is the time taken for a material do degrade to half its current radioactivity, so from 100 to 50, then to 25 then to 12.5 then to 6.25, ect.