p(t)=100(21)2.0373tRadioactive isotopes are unstable atoms that decay into other atoms. Oxygen−15 is a radioactive isotope. The function models p, the percentage of oxygen−15 atoms remaining in a sample after t minutes. Which of the following statements is the best interpretation of the ordered pair (4.0746,25) ?Choose 1 answer:(A) About 25 percent of oxygen−15 atoms remain in a sample after 4.0746 minutes.(B) About 4.0746 percent of oxygen−15 atoms remain in a sample after 25 minutes.(C) About 25 percent of oxygen−15 atoms in a sample decay into other atoms in 4.0746 minutes.(D) About 4.0746 percent of oxygen−15 atoms in a sample decay into other atoms in 25 minutes.
Q. p(t)=100(21)2.0373tRadioactive isotopes are unstable atoms that decay into other atoms. Oxygen−15 is a radioactive isotope. The function models p, the percentage of oxygen−15 atoms remaining in a sample after t minutes. Which of the following statements is the best interpretation of the ordered pair (4.0746,25) ?Choose 1 answer:(A) About 25 percent of oxygen−15 atoms remain in a sample after 4.0746 minutes.(B) About 4.0746 percent of oxygen−15 atoms remain in a sample after 25 minutes.(C) About 25 percent of oxygen−15 atoms in a sample decay into other atoms in 4.0746 minutes.(D) About 4.0746 percent of oxygen−15 atoms in a sample decay into other atoms in 25 minutes.
Plug in t=4.0746: Plug in t=4.0746 into the function p(t) to see if it equals approximately 25.p(t)=100(21)(2.0373t)p(4.0746)=100(21)(2.03734.0746)
Calculate the exponent: Calculate the exponent first: (4.0746)/(2.0373).4.0746/2.0373≈2
Calculate (21)2: Now calculate (21)2.(21)2=41
Multiply the result: Multiply the result by 100 to find the percentage.100×41=25
Interpret the result: Since p(4.0746)=25, the ordered pair (4.0746,25) means that about 25 percent of oxygen-15 atoms remain after 4.0746 minutes.
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