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The function f(x)=500(0.5)^x/100 models the amount of pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.

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Answer:

the amount of radioactive material in the vault after 140 years is 190 pounds.

Step-by-step explanation:

The given model for the amount of pounds of a particular radioactive material is

f(x) = 500(0.5)^(x/100)

where

  • x is the number of years since the material was put into the vault
  • f(x) is the amount of pounds of the material

Therefore,  the amount of radioactive material in the vault after 140 years will be

f(140)  = 500(0.5)^(140/100)

f(140)  = 189.5 pounds

This answer rounded off to the nearest whole number will be

f(140) = 190 pounds

Therefore, the amount of radioactive material in the vault after 140 years is 190 pounds.

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