1.
An ancient discovery found a sample, where 75% of the original carbon (C14\text{C}^{14}) remains. Then the age of the sample is [T1/2(C14)=5730T_{1/2}(\text{C}^{14}) = 5730 years, ln0.5=0.7\ln 0.5 = -0.7,\ ln(0.75)=0.3\ln(0.75) = -0.3]