Question 378561
The formula for determining the amount of substance left is {{{A = Ce^(kt)}}}, where C is the initial amount, k is the decay constant, and t is time. We must solve for k:

Given the half-life of 432 years, we may plug in t:

{{{C/2 = Ce^(432k)}}}

{{{1/2 = e^(432k)}}}

Taking ln of both sides,

{{{ln (1/2) = 432k}}}

{{{k = (ln (1/2))/432}}} = -0.00160...

Now, we substitute t = 343 years to our equation to obtain

{{{A = 45*e^(343*-.00160)}}} = 25.95376 (grams)