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)

Respuesta :

[tex]y=a(0.5)^{\frac{t}{h}}[/tex]

a = 970 grams

y = 98 grams

t = ?

h = 13 minutes

Therefore,

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