Question

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?

Answer 1

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

Answer 2

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

Answer 3

how exactly would you do that?

Answer 4

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

Answer 5

i dont quite understand