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 how many years?

Question

Mathematics

Vanessa Cardenas

15 May, 03:51

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 how many years?

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Goodman · Answer 1

Ending Amt = Bgng Amt * e ^-0.03t

In this equation, the "-0.03" is the decay factor or "k"

We can now solve for half-life by this equation:

t = (ln [y (t) : a]) : - k (we can say beginning amount = 200 and ending amount = 100

t = (ln [200 : 100]) : - k

t = (ln [2]) : - k

t = 0.69314718056 : - -.03

t = 23.1049060187

about 23 years