Choose the one alternative that best completes the statement or answers the question.
-The function $f ( x ) = 300 ( 0.5 ) ^ { x / 90 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 200 years. Round to the nearest whole number.
A) 333 pounds
B) 220 pounds
C) 68 pounds
D) 64 pounds

Question

Quizplus · Accepted Answer

To find the amount of radioactive material after 200 years, substitute $x = 200$ into the function: $f(200) = 300(0.5)^{200/90}$. This simplifies to $f(200) = 300(0.5)^{2.222}$. Calculating this gives approximately 64 pounds.

Choose the One Alternative That Best Completes the Statement or Answers