Question

6. The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of Maui in Hawaii is no longer active.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 62.31% of its original carbon-14. The half-life of carbon-14 is 5730 years. a. Use the exponential decay formula Q(t) = Q,e to find the rate of decay, k. Round k to four decimal places. b. Write the exponential decay function for the Lualailua Hills Qudrangle volcano. c. Using the chemical analysis conducted by the scientists, determine how long ago the last eruption of the volcano occurred.

Answer 1

Q(t) = Qo e^- kt

Half life = 5730 years

1/2 Qo = Qo e^(- 5730 k )

1/2 = e^(- 5730 k )

k = 0.0001

Decay rate k = 0.0001

b)

Function is

Q(t) = Qoe-0.00011

c)

Plug Q(t) = .6231 Qo

.6231 Qo = Qo e^- 0.0001t

Dividing both sides by Qo

0.6231 = e^- 0.0001t  

t = 4730

Last eruption of volcano occured 4730 years ago