Kennedy W.

asked • 11/08/15

Algebra help please?

An anthropologist finds bone that her instruments measure it as 0.146% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.

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Hassan F. answered • 11/08/15

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Let's first make a table of several consecutive half lives and how many half-lives it takes to reach 0.146% of initial value:
 
Time 0               100%
1st half life         50%
2nd half life        25%
3rd half life        12.5%
4th half life         6.25%
5th half life         3.125%
6th half life        1.5625%
7th half life       0.78125%
8th half life      0.390625%
9th half life      0.1953%
10th half life    0.09765%
 
0.146% is about half way between the 9th and 10th half lives. So we can say it is about 9.5 half lives
 
If each half life is 5730 years, then 9.5 * 5730 = 54435 years is how long it was when the person died
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Kennedy W.

Thank you so much, would you happen to know the answer to these?
1. A radio active isotope decays according to the exponential decay equation where t is in days.

Round to the thousandths place.

For the half life: The half life is the solution (t) of the equation : a2=ae^−6.345t
 
2. Zeus Industries bought a computer for $2538. It is expected to depreciate at a rate of 20% per year. What will the value of the computer be in 4 years?


Round to the nearest penny. Do not type the "$" sign in your answer
 
3. A radio active isotope decays according to the exponential decay equation where t is in days.

Round to the thousandths place.

For the half life: The half life is the solution (t) of the equation : a2=ae^−7.571t
 
4. An anthropologist finds bone that her instruments measure it as 0.177% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand. 
 
5. The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $4.0 trillion?
 
6. The Mendes family bought a new house 8 years ago for $126,000. The house is now worth $156,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Round your answer to the nearest tenth of a percent (1.2% etc)
 
 
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11/08/15

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