carbon - 14 is a radioactive isotope used to determine the age of samples of organic matter. the amount of…
carbon - 14 is a radioactive isotope used to determine the age of samples of organic matter. the amount of carbon - 14 in a sample decreases once the organism is no longer alive. the half - life of carbon - 14 is approximately 5730 years. this means that every 5730 years, the amount of carbon - 14 in an organism that is no longer living will be halved. which of the following functions, c, models the fraction of carbon - 14 remaining in a sample after t years? choose 1 answer: a $c(t)=2^{\frac{t}{5730}}$ b $c(t)=(\frac{1}{2})^{\frac{t}{5730}}$ c $c(t)=(\frac{1}{2})^{5730t}$ d $c(t)=2^{5730t}$
Answer
Explanation:
Step1: Recall half - life formula
The general formula for exponential decay with half - life $h$ is $C(t)=C_0\left(\frac{1}{2}\right)^{\frac{t}{h}}$, where $C_0$ is the initial amount, $t$ is the time elapsed, and $h$ is the half - life. In the case of finding the fraction of the remaining substance, we can assume $C_0 = 1$.
Step2: Identify values for this problem
The half - life $h$ of carbon - 14 is 5730 years. Substituting $C_0 = 1$ and $h=5730$ into the formula $C(t)=C_0\left(\frac{1}{2}\right)^{\frac{t}{h}}$, we get $C(t)=\left(\frac{1}{2}\right)^{\frac{t}{5730}}$.
Answer:
B. $C(t)=\left(\frac{1}{2}\right)^{\frac{t}{5730}}$