Question

question 18 (mandatory) (1 point) 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 $m(t)=300(\frac{1}{2})^{\frac{t}{24}}$. what mass will remain after 31 days? a) 177.5 g b) 122.5 g c) 193.75 g d) 150 g

Explanation:

Step1: Identify the values to substitute

We know $M(t)=300(\frac{1}{2})^{\frac{t}{24}}$, and $t = 31$.

Step2: Substitute $t = 31$ into the formula

$M(31)=300(\frac{1}{2})^{\frac{31}{24}}$

Step3: Calculate the exponent value

$\frac{31}{24}\approx1.2917$

Step4: Calculate $(\frac{1}{2})^{\frac{31}{24}}$

$(\frac{1}{2})^{1.2917}\approx0.4083$

Step5: Calculate $M(31)$

$M(31)=300\times0.4083 = 122.49\approx122.5$

Answer:

B. 122.5 g