Question

Exponential decay occurs with radioactive substances.  This fact can help scientists estimate the age of objects.  All living creatures contain carbon.  Some of that carbon is in the form of radioactive Carbon-14.  Since it is radioactive, carbon-14 decays.  This substance decays fairly slowly;  it decreases by approximately 1.202% every 100 years.  If an archeologist unearthed a fossil of a once living creature, the amount of carbon-14 remaining in that fossil would help the archeologist calculate the number of years since the creature died.  This is called carbon dating.  If a fossil contained 75% of the original carbon-14, how old is the fossil?  Solve using logarithms and round to 2 decimal places.  Answer is in 100s of years so multiply your result by 100.  Enter your final result with no decimal places.

Answer 1

Explanation:

1.202 % decay means 98.798 % remains...or .98798 in decimal

( .98798)^n = .75 where 'n' is the number of hundreds of years

LOG both sides

n LOG .98798 = LOG ( .75)

n = 23.79 ( rounded to two decimal places)

23.79 x 100 = 2379 years