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If a radioactive substance is quickly decaying at a rate of 13 percent per hour, approximately how much of a 200-pound sample remains after one day?

A) 26 pounds
B) 52 pounds
C) 104 pounds
D) 156 pounds

Answer :

Final answer:

To find out how much of a 200-pound radioactive sample remains after one day when it decays at a rate of 13 percent per hour, you calculate the exponential decay over 24 hours to find that approximately 26 pounds remain, corresponding to option A.

Explanation:

If a radioactive substance is quickly decaying at a rate of 13 percent per hour, the amount of the substance remaining after a given time can be calculated using the formula for exponential decay:

[tex]A = P(1 - r)^t[/tex]

where:

A is the amount remaining after time t,

P is the initial amount of the substance,

r is the decay rate per unit time,

t is the number of time units that have passed.

For a 200-pound sample that decays at 13 percent per hour:

Convert the decay rate to decimal form: 0.13

Calculate the remaining amount after one hour: [tex]A = 200(1 - 0.13)^1[/tex]

Since one day is 24 hours, calculate the remaining amount after 24 hours: [tex]A = 200(1 - 0.13)^2^4[/tex]

After performing the calculation, the amount of the substance remaining after one day is approximately 26 pounds, making the answer to the question option A).

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