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.

Question

Mathematics

Kiara Hart

4 May, 09:32

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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Answers (1)

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Armani · Answer 1

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.