A 40 gram sample of a radioactive isotope decays at a rate of 2.5% annually. What is the exponential function that models the decay? What is the half life of this isotope? How much will be present after 65 years?

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A 40 gram sample of a radioactive isotope decays at a rate of 2.5% annually. What is the exponential function that models the decay? What is the half life of this isotope? How much will be present after 65 years?

Mathematics
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\[P _{t} = P _{0} (1-r)^{kt}\] P0 = 40 r = 0.025 k = constant t = time
in this case k=1 for half life set Pt = 20 and solve for t
how exactly would you do that?

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Other answers:

use logs \[20 = 40(.975)^{t}\] \[\frac{\log_{} (1/2) }{\log_{} (0.975)} = t\]
i dont quite understand

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