Assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of thesubstance to disintegrate. Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in South Africa along with the remains of a campfire.Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.Complete parts (a) through (e) below.(a) Estimate the age of the skull if the half-life of carbon-14 is about 5690 years.The skull is about years old.(Round to the nearest whole number as needed.)(b) Estimate the age of the skull if the half-life of carbon-14 is about 5590 years.The skull is about years old.(Round to the nearest whole number as needed.)(c) Compare the answers to parts (a) and (b). Choose the correct answer below.O A. The answer to part (b) is less than the answer to part (a). Decreasing the half-life decreases the age of the skull. The change in the age of the skull here is much less than the change inthe half-life,O B. The answer to part (b) is greater than the answer to part (a). Decreasing the half-life increases the age of the skull. The change in the age of the skull here is much greater than thechangethe half-life.O C. The answer to part (b) is less than the answer to part (a). Decreasingchange in the half-life,half-life decreases the age of the skull. The change in the age of the skull here is much greater than theO D. The answer to part (b) is greater than the answer to part (a). Decreasing the half-life increases the age of the skull. The change in the age of the skull here is much less than the changein the half-life.(d) Estimate the age of the skull if the half-life of carbon-14 is about 5690 years and 3% of the original amount of carbon-14 remains in the burnt wood of the campfire.The skull is about years old.(Round to the nearest whole number as needed.)(e) Compare the results of the previous parts. Choose the correct answer below.O A. The answer to part (d) is less than the answer to part (a). Increasing the percent remaining by one percent decreases the age of the skull by a minimalO B. The answer to part (d) is greater than the answer to part (a). Increasing the percent remaining by one percent increases the age of the skull by a minimalOC. The answer to part (d) is greater than the answer to part (a). Increasing the percent remaining by one percent greatly increases the age of the skull.O D. The answer to part (d) is less than the answer to part (a). Increasing the percent remaining by one percent greatly decreases the age of the skull.

Question

Accepted Answer

It is given that only 2% of the original amount of carbon-14 remains in the burnt wood.