## anonymous 5 years ago 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?

1. anonymous

$P _{t} = P _{0} (1-r)^{kt}$ P0 = 40 r = 0.025 k = constant t = time

2. anonymous

in this case k=1 for half life set Pt = 20 and solve for t

3. anonymous

how exactly would you do that?

4. anonymous

use logs $20 = 40(.975)^{t}$ $\frac{\log_{} (1/2) }{\log_{} (0.975)} = t$

5. anonymous

i dont quite understand