The half-life of carbon-14 is 5730 years. How long will it take for 7/8 of a sample of carbon-14 to decay? 11,460 years 17,190 years 22,920 years 28,650 years

The formula for exponential decay is P_1=P_0*e^-kt. If the half-life is 5730 years, then:
.5=e^-5730k
ln .5=ln e^-5730k=-5730k ln e= -5730k
k=.00012096809
0.125=e^.00012096809t
ln 0.125=ln e^.00012096809t=.00012096809t ln e=-0.00012096809t
t=17,190 years

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swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-05-03T15:13:57+02:00

The half-life of carbon-14 is 5730 years and It takes 7/8 of a sample of carbon-14 to decay is 17190 years.

We have given,

The half-life of carbon-14 is 5730 years.

What is the formula of exponential decay?

The formula for exponential decay is,

[tex]P_1=P_0*e^{-kt}.[/tex]

If the half-life is 5730 years, then

[tex]0.5=e^{-5730k}[/tex]

[tex]ln .5=ln e^{-5730k}=-5730k ln e= -5730k[/tex]

[tex]k=0.00012096809[/tex]

[tex]0.125=e^{0.00012096809t}[/tex]

ln 0.125=ln e^.00012096809t

=.00012096809t ln e

=-0.00012096809t

t=17,190 years

Therefore, it takes for 7/8 of a sample of carbon-14 to decay is 17190 years.

To learn more about the decay visit:

https://brainly.com/question/25802424 #SPJ3