Solve the problem. 14) On e method to determine the time since an animal died is

Question

Solve the problem. 14) On e method to determine the time since an animal died is to estimate the its bones. The half-life of carbon-14 is 5730 years. percentage of cartbon-14 remaining in percentage of carbon-14 remaining in a. Approximate (to the nearest year) the age of a fossil if there is only 25% of the carbon-14 remaining, b. Approximate (to the nearest year) the age of a fossil if there is only 1% of the carbon-14 remaining.

Explanation / Answer

Dear Student Thank you for using Chegg !! Present Quantity = 25 % Half Life = 5730 years A (t) = A0 e^ -kt A (t) is present quantity A0 is initial quantity t is time period k is decay rate Since Given Half Life => A(t) = A0/2 A0/2 = A0e^(-k*5730) 0.5 = e^(-k*5730) Taking Natural Log Both sides -0.693147181 = -k*5730 k = 0.000120968 A) Now using this k, calcuating time taken for Carbon -14 to decay to 25% i.e. A(t) = A0/4 A0/4 = A0e^(-k*t) 0.25 = e^(-k*t) Taking Natural Log Both sides -1.386294361 = -kt t = 11460 years Solution b) Now using this k, calcuating time taken for Carbon -14 to decay to1% i.e. A(t) = A0/100 A0/100 = A0e^(-k*t) 0.01 = e^(-k*t) Taking Natural Log Both sides -4.605170186 = -kt t = 38069.29597 years = 38069 years Solution

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