The amount of carbon 14 remaining in a sample that originally contained A grams is given by
C(t) = A(0.999879)t
where t is time in years. If tests on a fossilized skull reveal that 99.89% of the carbon 14 has decayed, how old, to the nearest 1,000 years, is the skull?

Question

The amount of carbon 14 remaining in a sample that originally contained A grams is given by
C(t) = A(0.999879)t
where t is time in years. If tests on a fossilized skull reveal that 99.89% of the carbon 14 has decayed, how old, to the nearest 1,000 years, is the skull?

campbell_st · Answer

so the initial value of A is 100

C(t) = 100 - 99.89

so 

C(t) = 0.11

using the formula 

$$0.11 =100(0.999879)^t$$

divide both side by 100

$$0.0011 = (0.999879)^t$$

take the log of both sides

$$\ln(0.0011) = t \times \ln(0.999879)$$

making t the subject

$$t = \frac{\ln(0.0011)}{\ln(0.999879)}$$

campbell_st · Answer

C(t) = 0.11 is the amount of carbon 14 left in the scull, as a percentage