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A radioactive substance decays at an ann...

A radioactive substance decays at an annual rate of 13 percent. If the initial amount of the substance is 325 grams, which of the following functions f models the remaining amount of the substance, in grams, t years later?

A

`f(t)=325(0.87)^(t)`

B

`f(t)=325(0.13)^(t)`

C

`f(t)=0.87(325)^(t)`

D

`f(t)=0.13(325)^(t)`

Text Solution

Verified by Experts

Choice A is correct. Each year, the amount of the radioactive substance is reduced by 13 percent from the prior year’s amount, that is, each year, 87 percent of the previous year’s amount remains. Since the initial amount of the radioactive substance was 325 grams, after 1 year 325(0.87) grams remains, after 2 years `325(0.87)(0.87)=325(0.87)^(2)` grams remains, and after t years, `325(0.87)^(t)` grams remains. Therefore, the function `f(t)=325(0.87)^(t)` models the remaining amount of the substance, in grams after t years.
Choice B is incorrect and may result from confusing the amount of the substance remaining with the decay rate. Choices C and D are incorrect and may result from confusing the original amount of the substance and the decay rate.
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