Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14 to decay to 10 percent of its original amount?

Carbon-14 will take 19,035 years to decay to 10 percent.

Step-by-step explanation:

Exponential Decay Function

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

Where:

No  = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

    = The decay constant.

One important parameter related to radioactive decay is the half-life:

If we know the value of the half-life, we can calculate the decay constant:

Carbon-14 has a half-life of 5,730 years, thus:

The equation of the remaining quantity of Carbon-14 is:

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

Simplifying:

Taking logarithms:

Solving for t:

Carbon-14 will take 19,035 years to decay to 10 percent.

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