SAT Mathematics Practice Test 2

Question : 14 of 58

Marks: +1, -0

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?

$f(t)=325(0.87)^t$
$f(t)=325(0.13)^t$
$f(t)=0.87(325)^t$
$f(t)=0.13(325)^t$

Validate

Solution:

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 years amount remains.Since the initial amount of the radio active substance was 325 grams,after 1 year .325(0.87) grams remains;after 2 years

325(0.87)(0.87)=325(0.84)^2

grams remains;and after

t

years,

325(0.87)^t

grams remains.Therefore ,the function

f(t)=325(0.87)^t

models the renaming 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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