anonymous
  • anonymous
A certain isotope decays so that the amount A remaining after t years is given by: A = A0 • e ^(-0.03t) where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is ____ years.
Mathematics
chestercat
  • chestercat
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Loser66
  • Loser66
Where are you stuck?
anonymous
  • anonymous
the entire thing! I dont even know how to start @Loser66
Loser66
  • Loser66
A = 1/2 A0, solve for t. Dat sit

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Loser66
  • Loser66
\(A_0\) is the original amount of the isotope, right?
Loser66
  • Loser66
\( A \) is the new amount of the original one, and it is = a half of original one. That means \(A=\dfrac{1}{2}A_0\)
Loser66
  • Loser66
Now, put them in, you have \(\dfrac{1}{2}A_0=A_0e^{-0.03t}\) simplify \(A_0\) and solve for t. I let you finish the stuff.
anonymous
  • anonymous
A=A0e^(-0.03t)

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