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).
