A farmer in china discovers a mammal hide that contains 71% of its original amount of C - 14.

Find the age of the mammal hide to the nearest year.

Guest Nov 16, 2018

#1**+1 **

71% =1 x (1/2)^(t/5730)

Solve for t :

0.71 = 2^(-t/5730)

0.71 = 71/100:

71/100 = 2^(-t/5730)

71/100 = 2^(-t/5730) is equivalent to 2^(-t/5730) = 71/100:

2^(-t/5730) = 71/100

Take reciprocals of both sides:

2^(t/5730) = 100/71

Take the logarithm base 2 of both sides:

t/5730 = log(100/71)/log(2)

Multiply both sides by 5730:

t = (5730 log(100/71))/log(2)=2831.24 =**~2,831 Years**

Guest Nov 16, 2018

#1**+1 **

Best Answer

71% =1 x (1/2)^(t/5730)

Solve for t :

0.71 = 2^(-t/5730)

0.71 = 71/100:

71/100 = 2^(-t/5730)

71/100 = 2^(-t/5730) is equivalent to 2^(-t/5730) = 71/100:

2^(-t/5730) = 71/100

Take reciprocals of both sides:

2^(t/5730) = 100/71

Take the logarithm base 2 of both sides:

t/5730 = log(100/71)/log(2)

Multiply both sides by 5730:

t = (5730 log(100/71))/log(2)=2831.24 =**~2,831 Years**

Guest Nov 16, 2018

#2**+1 **

Fo =1/2 ^(t/5730)

.71 = 1/2^(t/5730) take log of both sides

log(.71)/log(.5) = t/5730

t = 5730 * log (.71)/log(.5) =~~ 2831. years

ElectricPavlov
Nov 16, 2018