Question

Element X decays radioactively with a half life of 9 minutes. If there are 760 grams ofElement X, how long, to the nearest tenth of a minute, would it take the element todecay to 19 grams?y = a(.5)Answer:

Answer 1

$y=a(0.5)^{\frac{t}{h}}$$19=760(0.5)^{\frac{t}{9}}$$\frac{19}{760}=(0.5)^{\frac{t}{9}}$$0.025=2^{\frac{-t}{9}}$$\log _20.025=\frac{-t}{9}^{}$$t=-9\cdot\log _2(0.025)$$t=47.89\approx47.9$