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

2500 years

Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find t.

We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For let's just assume that there are 100 original  atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

Now, solve. First, divide by 100.

Take the log of everything

Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get

Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.

Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.