Answer:
B. 22.5 grams; exponential .
Step-by-step explanation:
We have been given that there is 360 grams of radioactive material with a half-life of 8 hours.
As amount of radioactive material remains 1/2 of the amount after each 8 hours, therefore, our function will be an exponential decay function.
We will use half-life formula to solve our given problem.
\(y=a*(\frac{1}{2})^{\frac{t}{b}}\), where,
\(a=\text{Initial value}\),
\(t=\text{Time}\),
\(b=\text{Half life}\).
Let us substitute a=360 and b=8 in half life formula to get half life function for our given radioactive material.
\(y=360*(\frac{1}{2})^{\frac{t}{8}}\), where y represents remaining amount of radioactive material after t hours.
Therefore, the function \(y=360*(\frac{1}{2})^{\frac{t}{8}}\) gives the half-life of our given radioactive material.
Let us substitute t=32 in our half life function to find the amount of material left after 32 hours.
\(y=360*(\frac{1}{2})^{\frac{32}{8}}\)
\(y=360*(\frac{1}{2})^{4}\)
\(y=360*\frac{1^4}{2^4}\)
\(y=360*\frac{1}{16}\)
\(y=22.5\)
Therefore, the radioactive material will be left 22.5 grams after 32 hours and the radioactive decay is modeled by an exponential function and option B is the correct choice.
