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]