Answer:
[tex]A\approx2.255 \text{ grams}[/tex]
Step-by-step explanation:
We can use the standard formula for half-life:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^\dfrac{t}{d}[/tex]
Where A₀ is the initial amount, d is the time for one half-life, and t is the number of days.
Because the half-life is 24.3 days, d = 24.3:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^\dfrac{t}{24.3}[/tex]
We want to find the amount of a 3-gram sample after 10 days. Hence, substitute and evaluate:
[tex]\displaystyle \begin{aligned} A & = (3)\left(\frac{1}{2}\right)^\dfrac{(10)}{24.3} \\ \\ & \approx 2.255\text{ grams}\end{aligned}[/tex]
In conclusion, about 2.255 grams will remain afetr 10 days.
