Answer:
The correct answer is 6.25g.
Explanation:
The half-life of a radioactive isotope is given by the formula [tex]\bold{y = a(1 - b)^x}[/tex] where a is the initial amount of the substance, b is the decay factor, and x is the time elapsed (this is also known as the exponential decay function). We can define our values and substitute them into the equation.
Now, if we place this into the equation, we can solve for the amount of carbon-14 that will remain after it radioactively decays four times.
[tex]y = 100.0(1 - 0.5)^4\\\\y = 100(0.5)^4\\\\y = 100(0.0625)\\\\y = 6.25[/tex]
Because you are given 3 significant figures in the problem (100.0), we don't need to round 6.25g up or down.
Note: Remember to apply your BPEMDAS ruling when simplifying the equation. Therefore, you should simplify your work in the parentheses first. Then, evaluate the solved value and raise it to the power of the exponent. Finally, you can distribute your initial value and solve for y.
