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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

2 Answers

3 votes

Answer:

B. 22.5 grams; exponential .

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*((1)/(2))^{(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*((1)/(2))^{(t)/(8)}, where y represents remaining amount of radioactive material after t hours.

Therefore, the function
y=360*((1)/(2))^{(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*((1)/(2))^{(32)/(8)}


y=360*((1)/(2))^(4)


y=360*(1^4)/(2^4)


y=360*(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.

User Hoju
by
8.1k points
6 votes
B.) 22.5 GRAMS, EXPONENTIAL

32 hours ÷ 8 hours = 4

The radioactive material will half 4 times.

360 x (1/2)⁴ = 22.50

360 x 1/2 = 180
180 x 1/2 = 90
90 x 1/2 = 45
45 x 1/2 = 22.50
User Jaygooby
by
8.8k points

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