Question

Initially there are 700 grams of a radioactive substance on hand. Suppose the half-life of the substance is 7 hours. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance?

Answer 1

We consider radioactive decay to exhibit first order kinetics. Moreover, we take the concentration of the radioactive nuclides to be their mass given.

Recall,

`ln[A]_"t" = -kt + ln[A]_0`, and by extension,

`t_(1/2) = ln(2)/k`

Let's derive the rate constant, first.

`7"h" = ln(2)/k`

`therefore k approx 9.9*10^-2"h"^-1`

With your format, we would come up with,

`A(t) = [A]_0e^(-kt)`, and in Excel,