[+rep] Exponential Decay problems

[Leet]

FIRST PROBLEMIn the fifth century, King Arthur sat at the huge round table. A table alleged to have belonged to King Arthur was found in England. In 1976, carbon dating revealed that the amount of radiocarbon left in the table was 91%. Could this table have belonged to King Arthur?

Half life of Carbon-14 = 5730 years.

SECOND PROBLEMProfessor James's body was found slumped over a stack of exams with red marks on them. A coroner came at noon and immediately took the temperature of the body. It is 94.6 degrees. After waiting one hour, she took the temperature again and found it to be 93.4 degrees. The temperature of the room is 70 degrees. When was the murder committed?

Let normal body temperature be 98.6 degrees.
Show work/explanation/calculations for both for full rep. Thanks.

For whomever solves 'em, I will also draw a picture :D

[bamag]

Leet Not sure if I did 2nd one correctly but I'm pretty sure about #1
1.
A(T) = Ao * e^(kT)
.5A = A * e^(kT)
.5 = e ^ (kT)
ln .5 = kT
-.693 = 5730k
k = -.000121
.91 =e^(-.000121T)
ln .91 = -.000121T
-.0943 = -.000121T
T= 779.4 years
The table could not have belonged to King Arthur.

2.
A(T) = Ao * e^(kT)
93.4=94.6 * e^(kT)
.987 = e^(kT)
ln .987 = k(1)
-.0131 = k
94.6 = 98.6 * e ^ (kT)
.96 = e^(kT)
ln .96 = kT
-.041 = -.0131T
T= 3.1
Noon - 3.1 = ~9AM