• The sample is decaying.
• The initial amount of the sample is 735 grams.
• The sample decays to 91.875 grams after 3 years.
The function f (x) = 735 (1/2)^x models the number of grams in a sample of a radioactive substance after x years. Which statements are true about the sample? Select all that apply.
• The sample is growing.
• The sample is decaying.
• The sample grows to 5,880 after 3 years.
• The initial amount of the sample is 735 grams.
• The sample decays to 91.875 grams after 3 years.
3 answers
explain
In this case, the function f(x) = 735(1/2)^x represents exponential decay, not growth. The coefficient of (1/2) means that the sample is decreasing in size over time.
The initial amount of the sample is 735 grams, as shown by the coefficient in front of the exponential term.
After 3 years, the amount of the sample is given by f(3) = 735(1/2)^3 = 735(1/8) = 91.875 grams. This shows that the sample has decayed to 91.875 grams after 3 years, which verifies the decay behavior of the sample.
Therefore, the correct statements are:
• The sample is decaying.
• The initial amount of the sample is 735 grams.
• The sample decays to 91.875 grams after 3 years.
The initial amount of the sample is 735 grams, as shown by the coefficient in front of the exponential term.
After 3 years, the amount of the sample is given by f(3) = 735(1/2)^3 = 735(1/8) = 91.875 grams. This shows that the sample has decayed to 91.875 grams after 3 years, which verifies the decay behavior of the sample.
Therefore, the correct statements are:
• The sample is decaying.
• The initial amount of the sample is 735 grams.
• The sample decays to 91.875 grams after 3 years.
1 answer