Answer:
A = 0.75 gram or 1 gram
Step-by-step explanation:
The half-life of carbon 14 is years. How much would be left of an original -gram sample after 2,292 years? (To the nearest whole number).
We can use the following formula for half-life of [tex]^{14}C[/tex] to find out how much is left from the original sample after 2,292 years:
[tex]A = A_{0}e^{-0.000124t}[/tex]
where:
A is the amount left of an original gram sample after t years, and
[tex]A_{0}[/tex] is the amount present at time t = 0.
The half-life of [tex]^{14}C[/tex] is the time t at which the amount present is one-half the amount at time t = 0.
If 1 gram of [tex]^{14}C[/tex] is present in a sample,
Solve for A when t = 2,292:
Substituting [tex]A_{0}[/tex] = 1 gram into the decay equation, and we have:
[tex]A = A_{0}e^{-0.000124t}[/tex]
[tex]A = A_{0}e^{-0.000124(2,292)}[/tex]
A = 0.75 g or 1 g
