body she finds that it is 80F The temperature of the room in

body, she finds that it is 80°F. The temperature of the room in which the body is found is 65°F. If the detective uses Newton\'s law of cooling. T(t) TA (T-T014, what will she say was the time of death? 7. An archeologist finds an artifact that contains 44% of the carbon-14 that it would have had originally. What is the estimated age of the artifact? (The half-life of carbon-14 is 5,730 years.)

Solution

6) T(t) = Ta + ( To - Ta ) e^-0.1947t

assuming initial temperature of body = 98.6 degrees F

Ta = 65 , T(t) = 80 , To = 98.6

plugging the values we get

80 = 65 + ( 98.6 - 65 ) e^-0.1947t

80 = 65 + 33.6 e^ -0.1947t

80 - 65 = 33.6 e^-0.1947t

15 / 33.6 = e^-0.1947t

t = 4.1421

so the time of death would be around 10pm

7) (1/2)^n = 0.44

where n is number of half lives

n = 1.1844

estimated age of artifact is

5730 * 1.1844

= 6786.753 years