if the half-life of an isotope is 7.6 minutes, how many grams will remain after 12.4 minutes if you started with 80 grams?

We have

40 = 80e^(7.6k)    solve for k

divide both sides by 80

.5 = e^(7.6k)    take the ln of both sides

ln.5 = lne^(7.6k)  and we can write

ln.5 = (7.6k)lne    and lne = 1

ln.5 = 7.6k  divide both sides by 7.6

ln.5/7.6 = k = about -.0912

So, after 12.4 minutes, we have

80e^(12.4 * -.0912) = about 25.82 g