Question

Element X decays radioactively with a half life of 13 minutes. If there are 970 gramsof Element X, how long, to the nearest tenth of a minute, would it take the element todecay to 98 grams?Y == a(.5)

Answer 1

`y=a(0.5)^{(t)/(h)}`

a = 970 grams

y = 98 grams

t = ?

h = 13 minutes

Therefore,

`\begin{gathered} 98=970(0.5)^{(t)/(13)} \\ (98)/(970)=(0.5)^{(t)/(13)} \\ 0.10103092783=(0.5)^{(t)/(13)} \\ \log _{}0.10103092783=\log _{}(0.5)^{(t)/(13)} \\ \log _{}0.10103092783=(t)/(13)*-0.30102999566 \\ \log _{}0.10103092783=-0.02315615351 \\ -0.99554565859=-0.02315615351t \\ t=(-0.99554565859)/(-0.02315615351) \\ t=42.9927042143 \\ t\approx43.0\text{ minutes} \end{gathered}`