This process can be modeled by the next formula:
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{1/2_{}_{}}}}[/tex]where N(t) is the quantity of the substance remaining, N0 is the initial quantity of the substance, t is the time elapsed, and t1/2 is the half-life of the substance.
Substituting with N0 = 960 grams, t = 500 days, and t1/2 = 250 days, we get:
[tex]\begin{gathered} N(t)=960\cdot(\frac{1}{2})^{\frac{500}{250}} \\ N(t)=960\cdot(\frac{1}{2})^2 \\ N(t)=960\cdot\frac{1}{4} \\ N(t)=240\text{ grams} \end{gathered}[/tex]There will be 240 grams
