p(m)=100((1)/(2))^((m)/( 27)) Bismuth-199 is a radioactive isotope that decays over time. The half-life of a radioactive isotope is the amount of time it takes for (1)/(2) of the isotopes in a sample to decay. The function models the percent of bismuth-199 remaining in a sample after m minutes. What is the meaning of the number 27 in the function? Choose 1 answer: (A) The amount of bismuth- 199 in the sample decreases by 27% every (1)/(2) minute. (B) The sample is initially composed of 27% bismuth- 199 . (C) The half-life of bismuth-199 is 13.5 minutes. (D) The half-life of bismuth-199 is 27 minutes.

Question

p(m)=100((1)/(2))^((m)/( 27)) Bismuth-199 is a radioactive isotope that decays over time. The half-life of a radioactive isotope is the amount of time it takes for  (1)/(2) of the isotopes in a sample to decay. The function models the percent of bismuth-199 remaining in a sample after  m minutes. What is the meaning of the number 27 in the function? Choose 1 answer: (A) The amount of bismuth- 199 in the sample decreases by  27% every  (1)/(2) minute. (B) The sample is initially composed of  27% bismuth- 199 . (C) The half-life of bismuth-199 is 13.5 minutes. (D) The half-life of bismuth-199 is 27 minutes.

Bytelearn · Accepted Answer

Understand function p(m): Understand the function p(m)=100((1)/(2))^((m)/(27)) and identify what each part represents. The function p(m) represents the percent of bismuth-199 remaining after m minutes. The base (1/2) indicates that we are dealing with a half-life decay process. The exponent (m/27) suggests that the time m is being scaled by a factor related to the half-life.Analyze options given: Analyze the options given to determine which one correctly describes the number 27 in the function. Option (A) suggests that the amount of bismuth-199 decreases by 27% every half minute, which is not indicated by the function. The function shows a half-life decay, not a percentage decrease per time unit.Continue analyzing options: Continue analyzing the options. Option (B) suggests that the sample is initially composed of 27% bismuth-199, which is not related to the number 27 in the exponent and does not make sense in the context of the function.Analyze option (D): Continue analyzing the options. Option (C) suggests that the half-life of bismuth-199 is 13.5 minutes. This would mean that the exponent should be (m/13.5) to represent the half-life in the function, which is not the case.Analyze option (D). Option (D) suggests that the half-life of bismuth-199 is 27 minutes. This aligns with the function because the exponent (m/27) means that every time m equals 27, the quantity of bismuth-199 is halved. Therefore, the number 27 represents the half-life of bismuth-199 in minutes.

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