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Carbon-14 is used for archaeological carbon dating. Its half-life is 5,730 years. How much of a 250g sample of carbon-14 will be left in 5,000 years? Write your answer rounded to the nearest hundredth.

Respuesta :

opudodennis

Answer:

136.54 grams

Step-by-step explanation:

-This is an exponential decay problem of a radioactive element of the form:

[tex]A=A_oe^{-rt}\\\\A_o=Initial \ size\\A=Size \ after\ t\ years\\t=time \ in \ years\\r=Rate \ of \ decay[/tex]

#Given the initial size is 250g, and the half life is 5730 years, size after 5000 yrs can be calculated as:

[tex]0.5A_o=A_oe^{-5730r}\\\\0.5=e^{-5730r}\\\\r=0.00012097\\\\\therefore A=A_oe^{-0.00012097t}\\\\=250e^{-0.00012097\times 5000}\\\\=136.54038\approx 136.54\ g[/tex]

Hence, the size of the element after 5000 days is 136.54 grams

darchae2014

Answer:

88.61

Step-by-step explanation:

This problem requires two main steps. First, we must find the decay constant k. If we start with 100g, at the half-life there will be 50g remaining. We will use this information to find k. Then, use that value of k to help us find the amount of sample that will be left in 1,000 years.

Identify the variables in the formula.

In 1,000 years, there will be approximately 88.61g remaining.

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