In the formula A(t) $A ( t ) = A _ { n e <sup>k t </sup>> }$ , A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. 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?
Carbon-14 decays at the rate of 0.0125% annually. Round to the nearest year, if necessary.

Question

In the formula A(t)

A ( t ) = A _ { n e <sup>k t </sup>&gt; }

, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. 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?
Carbon-14 decays at the rate of 0.0125% annually. Round to the nearest year, if necessary.

Quizplus · Accepted Answer

The formula for decay is $A(t) = A_0 e^{kt}$. Given that 59% of the original carbon-14 remains, we have $0.59 = e^{kt}$. The decay rate is 0.0125% annually, so $k = -0.000125$. Solving for $t$, we get $t \approx 4221$ years.

In the Formula A(t) A ( t ) = A _ { n e <sup>k t </sup>&gt; }

In the Formula A(t) $A ( t ) = A _ { n e <sup>k t </sup>> }$