If there is 360 grams of radioactive material with a half-life of 8 hours, how much of the radioactive material will be left after 32 hours and is the radioactive decay modeled by a linear function or an exponential function?

a. 22.5 grams; linear

b. 22.5 grams; exponential

c.45 grams; linear

d. 45 grams; exponential

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.          

, where,

,

,

.

Let us substitute a=360 and b=8 in half life formula to get half life function for our given radioactive material.

, where y represents remaining amount of radioactive material after t hours.

Therefore, the function 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.

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.

do it yourself this is easy

step-by-step explanation: