SOLUTION: A lab has a sample of ore containing 500 mg of radioactive material. The radioactive material has a half-life of one day, so it takes one day for half the atoms in the substance to

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Question 1196812: A lab has a sample of ore containing 500 mg of radioactive material. The radioactive material has a half-life of one day, so it takes one day for half the atoms in the substance to decay.
A. Is this a geometric or arithmetic sequence?
B. Does it make a difference if you calculate the half-life at the beginning or end of the day? Explain.
C. What formula can you use to find the radioactive material in the sample at the beginning of the 7th day?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
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A. Is this a geometric or arithmetic sequence?
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Completely obvious!

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C. What formula can you use to find the radioactive material in the sample at the beginning of the 7th day?
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Initially before any time pass, 500 mg. of the radioactive material.
After one day (or one half-life), ;
AFTER two days (or two half-lives), ;
.
.
AFTER some number x days (x number of half-lives), of material remaining.

The beginning of day 7 is same as the end of day 6, so the amount present than would be .

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

This collection of words from the post

        "B. Does it make a difference if you calculate the half-life
              at the beginning or end of the day? Explain."

does not make any sense.

                    Consider it as my requested explanation.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

A. Is this a geometric or arithmetic sequence?

The amount of radioactive material remaining gets multiplied by 1/2 each day. That should make the answer obvious, if you know the definitions of arithmetic and geometric sequences.

B. Does it make a difference if you calculate the amount remaining at the beginning or end of the day? Explain.

From the beginning of any day to the end of the day, the amount remaining gets cut in half; of course it makes a difference.

C. What formula can you use to find the radioactive material in the sample at the beginning of the 7th day?

The beginning of the 7th day is the end of the 6th day. Assuming the amount is 500mg at the beginning of the first day (the problem doesn't say so...), the formula for the amount remaining at the beginning of the 7th day is .