Question

PLEASE HELP ME ASAP I NEED THIS BY 5:00

CLAIM EVIDENCE REASONING CONCLUSION:
Suppose you found a material in which 6.25% of the original radioactive atoms were present. If the half-life is 35 months, how old is the material?
● State your CLAIM (how old is the material?)
● Cite your EVIDENCE (what data did you use?)
● Explain your REASONING (how did you arrive at your answer?

Answer 1

CLAIM: The material is approximately 105 months (8.75 years) old.

EVIDENCE: The material contains 6.25% of the original radioactive atoms.

REASONING: We can use the formula for radioactive decay to calculate the age of the material. The formula is:

`N = N0 x (1/2)^(^t^/^T^)`

where N is the final amount of radioactive atoms, N0 is the initial amount of radioactive atoms, t is the time that has passed, and T is the half-life of the material.

We know that N = 0.0625 N0, since only 6.25% of the original radioactive atoms are present. We also know that T = 35 months, the given half-life. Substituting these values into the formula, we get:

`0.0625 N0 = N0 x (1/2)^(^t^/^3^5^)`)

Dividing both sides by N0, we get:

`0.0625 = (1/2)^(^t^/^3^5^)`

Taking the logarithm of both sides, we get:

`log 0.0625 = (t/35) log (1/2)`

Solving for t, we get:

`t = -35 x (log 0.0625) / (log 1/2)`

Using a calculator, we can evaluate the right-hand side of this equation to be approximately 105 months (8.75 years).

CONCLUSION: The material is approximately 105 months (8.75 years) old based on the evidence and reasoning presented above.

Answer 2

The material is approximately 119 months old. This is based on the fact that the half-life of a radioactive material is the time taken for the quantity of the material to decrease to half of its original amount. In this case, 6.25% of the original radioactive atoms were present, which means that the material has decreased to half its initial amount after 35 months. Therefore, it can be concluded that the material is approximately 119 months old (35 months * 3.4 = 119 months).

Hope this helps! Have a great day. :)