Question

select the correct answer. scientists found an animal skull during an excavation and tested the amount of carbon - 14 left in it. they found that 55 percent of the carbon - 14 in the skull remained. how many years ago was the animal buried? round your answer to nearest whole number. (hint: $a = a_0e^{- 0.000124t}$) a. 443,548 years b. 362,903 years c. 6,439 years d. 4,821 years

Explanation:

Step1: Set up the equation

We know that $A = 0.55A_0$ (since 55% of the carbon - 14 remains), and the formula is $A = A_0e^{- 0.000124t}$. Substitute $A = 0.55A_0$ into the formula:
$0.55A_0=A_0e^{-0.000124t}$. Divide both sides by $A_0$ (since $A_0
eq0$), we get $0.55 = e^{-0.000124t}$.

Step2: Take the natural logarithm of both sides

$\ln(0.55)=\ln(e^{-0.000124t})$. According to the property $\ln(e^x)=x$, the right - hand side simplifies to $- 0.000124t$. So, $\ln(0.55)=-0.000124t$.

Step3: Solve for $t$

$t=\frac{\ln(0.55)}{- 0.000124}$. We know that $\ln(0.55)\approx - 0.5978$. Then $t=\frac{-0.5978}{-0.000124}\approx4821$.

Answer:

D. 4,821 years