A 300 g sample of thorium -234 has a half-life of 24 days. The mass of thorium, in grams, that remains after t days can be modelled by M(t)=300((1)/(2))^(t)/(24) What mass will remain after 31 days? a) 122.5 g b) 193.75 g c) 1508 d) 177 .5g

## Step 1: Calculate the exponent<br />### The time elapsed is 31 days, and the half-life is 24 days. The exponent in the formula is $\frac{t}{24}$, so we calculate $\frac{31}{24} \approx 1.29$.<br /><br />## Step 2: Calculate the remaining mass<br />### Substitute $t=31$ into the given formula: $M(31) = 300 \cdot (\frac{1}{2})^{\frac{31}{24}} \approx 300 \cdot (\frac{1}{2})^{1.29} \approx 300 \cdot 0.41 \approx 123$.