1- This exercise uses the radioactive decay model. A wooden artifact from an anc

Question

1-

This exercise uses the radioactive decay model.

A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your decay rate, r, to 6 decimal places. Then round your answer to the nearest whole number.)
yr

2-

This exercise uses the radioactive decay model.

The burial cloth of an Egyptian mummy is estimated to contain 60% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest ten years.)
yr

3-

This exercise uses Newton's Law of Cooling.

Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 70°F.

(a) Find a function T(t) that models the temperature t hours after death.

(b) If the temperature of the body is now 76°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
hr

Explanation / Answer

1) half life = 5730 years

we can write decay function as

P = Po e^kt

1/2 Po = Po e^5730r

ln 1/2 = 5730 r

r = -.000121

ln.70 = -.000121 t

t = 2948

artifact was made 2948 years ago

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