5.–/1 points scalcet8 3.8.011. ask your teacher my notes question part points submissions used scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a parchment fragment was discovered that had about 74% as much 14c radioactivity as does plant material on earth today. estimate the age of the parchment. (round your answer to the nearest hundred years.) yr

Explanation:

These steps explain how you estimate the age of the parchment:

1) Carbon - 14 half-life: τ = 5730 years

2) Number of half-lives elapsed: n

3) Age of the parchment = τ×n = 5730×n years = 5730n

4) Exponential decay:

The ratio of the final amount of the radioactive isotope C-14 to the initial amount of the same is one half (1/2) raised to the number of half-lives elapsed (n):

5) The parchment fragment  had about 74% as much C-14 radioactivity as does plant material on Earth today:

Hence, 2.30 half-lives have elapsed and the age of the parchment is:

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step-by-step explanation:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2