SOLUTION: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists c

Algebra.Com
Question 1157950: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of
Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists
conducted a chemical analysis of samples from the volcano area. The samples
contained approximately 62% of its original carbon-14. How long ago was the last
eruption of the volcano? Use 5730 years for the half-life of carbon-14.
Work must be shown!
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
P=Poe^(-kt)
P/Po=1/2=e^(-kt)
-ln2=-kt
k=ln2/t
=0.693/5730
=0.000121
P/Po=0.62=e^(-0.000121*t)
ln(0.62)=-0.000121*t
t=3950.71 years
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

An equation of the radioactive decay in this case is 


     = ,


where C is the initial mass of carbon-14 in the sample; t is the time in years.


Simplify and solve for "t", which is the major unknown in this case.

Start canceling "C" in both sides.


     = 0.62


Take logarithm base 2 from both sides


    -t/5730 = 


    -t/5730 = -0.6897


    t = 5730*0.6897 = 3952 years    (rounded to closest integer value).      ANSWER


RELATED QUESTIONS

Mr. Wu’s biology class is writing group reports about the Hawaiian Islands. He has a... (answered by edjones)
A volcano that is currently about one-half mile below the surface of the pacific ocean... (answered by checkley71)
Flying to Maui with a tailwind a plane averaged 158km/h. On the return trip the plane... (answered by ptaylor)
Kilauea is an active shield volcano on the island of Hawai’i. The height of the volcano (answered by ikleyn,josgarithmetic,math_tutor2020)
Deception Island in Antarctica and Kilauea in Hawaii are two volcanoes that erupted in... (answered by josmiceli)
You are approaching the island of Hawaii in a small boat. The highest point on Hawaii is... (answered by tjnw79)
Eyjafjallajökull is a volcano in Iceland. During a recent eruption the volcano spewed... (answered by ikleyn)
Eyjafjallajokull is a volcano in Iceland. During a recent eruption, the volcano spewed... (answered by ikleyn)
Using the existing elevation of the Big Island of Hawaii, and an assumed lava flow-rate... (answered by oberobic)