A hiker in Africa discovers a skull that contains 32% of it's original amount of C-14. N = N0e^-kt. N0 = initial mass (at time t = 0) N = mass at time t. K = 0.0001. T = time, in days. Find the substance's half-time, in days. Find the substance's half-life, in days. Find the age of the skull to the nearest year

Question

A hiker in Africa discovers a skull that contains 32% of it's original amount of C-14.  N = N0e^-kt. N0 = initial mass (at time t = 0) N = mass at time t. K = 0.0001. T = time, in days. Find the substance's half-time, in days. Find the substance's half-life, in days. Find the age of the skull to the nearest year

Vocaloid · Answer

N = N0 * e^(-kt)

it's asking for the half-life, which is the point at which half the substance has decayed. therefore, N = (1/2)N0 and you can substitute to get:

(1/2)N0 = N0 * e^(-kt)

N0 cancels out from both sides

(1/2) = e^(-kt)

plug in k = 0.0001 and solve for t