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Carbon Dating Refer to Example. A sample from a refuse

Chapter 2, Problem 32A

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QUESTION:

Carbon Dating Refer to Example. A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 found in a contemporary living sample. How old was the sample?Half-Life Find the half-life of each radioactive substance. See Example.Carbon DatingCarbon-14 is a radioactive form of carbon that is found in all living plants and animals. After a plant or animal dies, the carbon-14 disintegrates. Scientists determine the age of the remains by comparing its carbon-14 with the amount found in living plants and animals. The amount of carbon-14 present after t years is given by the exponential equation with k = ?[(ln 2)/5600].(a) Find the half-life of carbon-14.SOLUTION Let A(t) = (1/2)A0 and k = ?[(ln 2)/5600]. The half-life is 5600 years.(b) Charcoal from an ancient fire pit on Java had 1/4 the amount of carbon-14 found in a living sample of wood of the same size. Estimate the age of the charcoal.SOLUTION Let A (t) = (1/4)A0 and k = ?[(ln 2)/5600]. The charcoal is about 11,200 years old.By following the steps in Example, we get the general equation giving the half-life T in terms of the decay constant k as For example, the decay constant for potassium-40, where t is in billions of years, is approximately ?0.5545 so its half-life is We can rewrite the growth and decay function asy = y0 ekt = y0(ek)t = y0 a t,where a = ek. This is sometimes a helpful way to look at an exponential growth or decay function.

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QUESTION:

Carbon Dating Refer to Example. A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 found in a contemporary living sample. How old was the sample?Half-Life Find the half-life of each radioactive substance. See Example.Carbon DatingCarbon-14 is a radioactive form of carbon that is found in all living plants and animals. After a plant or animal dies, the carbon-14 disintegrates. Scientists determine the age of the remains by comparing its carbon-14 with the amount found in living plants and animals. The amount of carbon-14 present after t years is given by the exponential equation with k = ?[(ln 2)/5600].(a) Find the half-life of carbon-14.SOLUTION Let A(t) = (1/2)A0 and k = ?[(ln 2)/5600]. The half-life is 5600 years.(b) Charcoal from an ancient fire pit on Java had 1/4 the amount of carbon-14 found in a living sample of wood of the same size. Estimate the age of the charcoal.SOLUTION Let A (t) = (1/4)A0 and k = ?[(ln 2)/5600]. The charcoal is about 11,200 years old.By following the steps in Example, we get the general equation giving the half-life T in terms of the decay constant k as For example, the decay constant for potassium-40, where t is in billions of years, is approximately ?0.5545 so its half-life is We can rewrite the growth and decay function asy = y0 ekt = y0(ek)t = y0 a t,where a = ek. This is sometimes a helpful way to look at an exponential growth or decay function.

ANSWER:

Solution:-Step 1 of 2Given thatWe have to find how old was the sample

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