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.
[tex]y=a*(\frac{1}{2})^{\frac{t}{b}}[/tex], where,
[tex]a=\text{Initial value}[/tex],
[tex]t=\text{Time}[/tex],
[tex]b=\text{Half life}[/tex].
Let us substitute a=360 and b=8 in half life formula to get half life function for our given radioactive material.
[tex]y=360*(\frac{1}{2})^{\frac{t}{8}}[/tex], where y represents remaining amount of radioactive material after t hours.
Therefore, the function [tex]y=360*(\frac{1}{2})^{\frac{t}{8}}[/tex] 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.
[tex]y=360*(\frac{1}{2})^{\frac{32}{8}}[/tex]
[tex]y=360*(\frac{1}{2})^{4}[/tex]
[tex]y=360*\frac{1^4}{2^4}[/tex]
[tex]y=360*\frac{1}{16}[/tex]
[tex]y=22.5[/tex]
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.
