Use the Gizmo to estimate the age of each of the objects below. For these questions, each second in the Gizmo represents 1,000 years. (8 pts) DescriptionAge (years) Egyptian papyrus with 63% of its original carbon-14 atomsAboriginal charcoal with 22% of its original carbon-14 atoms. Mayan headdress with 79% of its original carbon-14 atomsNeanderthal skull with 3% of its original carbon-14 atoms

Check the explanation

Explanation:

AT = A0 e (-T/H)

... where A0 is the starting activity, AT is the activity at some time T, and H is the half-life, in units of T.

Substituting what we know, we get ...

0.71 = (1) e (-T/5730)

Solve for T ...

loge (0.71) = - T/5730

T = - loge (0.71) (5730)

T = 1962 (conservatively rounded, T = 2000)

similarly for all

for aboriginal charcoal

0.28 = (1) e (-T/5730)

Solve for T ...

loge (0.28) = - T/5730

T = - loge (0.28) (5730)

T = 7294 (conservatively rounded, T = 7000)

for mayan headdress

0.89 = (1) e (-T/5730)

Solve for T ...

loge (0.89) = - T/5730

T = - loge (0.89) (5730)

T = 667 (conservatively rounded, T = 700)

for neanderthal

0.05 = (1) e (-T/5730)

Solve for T ...

loge (0.05) = - T/5730

T = - loge (0.05) (5730)

T = 17165 (conservatively rounded, T = 17000)