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Q: What is the equation to solve half life problems?
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How would the half life equation of aluminum be balanced differently?

The half-life equation for aluminum will be the same as the half-life equation for any other radioactive isotope, as it depends on the decay constant unique to that isotope. The balance is not dependent on the element itself, but rather on the specific isotope of that element.


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Generally speaking, life problems that are the easiest to solve are the ones you know how to solve. Even if the solution requires time or energy, you'll have a plan because you know what to do to get to the solution.Generally speaking, ANY problem is easiest to solve when you know how to solve it, whether in math, science, or daily life.


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


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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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