Carbon-14 is a radioactive substance with a half-life of about 5730 years and it can be used to date fossils. A Native American mummy was found recently and it was determine that it originally contained 5 milligrams of carbon-14.

A) Write an equation that models this situation.

B) After 3000 years, how much of the carbon-14 would remain?

Question

Carbon-14 is a radioactive substance with a half-life of about 5730 years and it can be used to date fossils. A Native American mummy was found recently and it was determine that it originally contained 5 milligrams of carbon-14.

A) Write an equation that models this situation.

B) After 3000 years, how much of the carbon-14 would remain?

anonymous · Answer

Since 5730 years is defined as the 1/2 life.  Set $$.5=e ^{(-5730)(x)}$$

Take the natural log of both sides.

$$\ln(.5)=lne ^{(-5730)(x)}$$

Which gives you .693=(x)(-5730)

So x= -.000129

anonymous · Answer

Let C equal carbon level today in mg. Let t= time in years

$$C=5e ^{-.000129t}$$

So at 3000 years, C = 3.395mg