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An artifact is discovered at a certain site. if it has 59% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)\

Respuesta :

0.59  = (1 - 0.000125)^^x    where x =  number of years of decay

ln 0.59  = x ln(0.999875)

x = 4221  to nearest year
raphealnwobi

The approximate age of the artifact is 0.059 years

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the amount of carbon-14 remaining after x years.

Carbon-14 decays at the rate of 0.0125% annually. Hence:

b = 0.0125% = 0.000125

Since it has 59% of the carbon-14 it originally contained. Hence y = 0.59a:

0.59a = a(0.000125)ˣ

0.59 = (0.000125)ˣ

ln(0.59) = xln(0.000125)

x = 0.059 years

Therefore the approximate age of the artifact is 0.059 years

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