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emmasim [6.3K]
3 years ago
13

Element X is a radioactive isotope such that every 25 years, its mass decreases by

Mathematics
2 answers:
marissa [1.9K]3 years ago
3 0

Answer:

It will take 25.6 years for the mass of the sample to reach 400 grams.

Step-by-step explanation:

Element X is a radioactive isotope such that every 25 years, its mass decreases by half.

This means that the amount of the substance after t years can be modeled by a function in the following format:

A(t) = A(0)(0.5)^{\frac{t}{25}}

In which A(0) is the initial amount.

Initial mass of a sample of Element X is 910 grams.

This means that A(0) = 910

So

A(t) = A(0)(0.5)^{\frac{t}{25}}

A(t) = 910(0.5)^{\frac{t}{25}}

How long would it be until the mass of the sample reached 400 grams?

This is t for which A(t) = 400

So

A(t) = 910(0.5)^{\frac{t}{25}}

400 = 910(0.5)^{\frac{t}{25}}

(0.5)^{\frac{t}{25}} = \frac{400}{910}

(0.5)^{\frac{t}{25}} = 0.43956

\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}

\frac{t}{25}\log{0.5} = \log{0.43956}

t = \frac{25\log{0.43956}}{\log{0.5}}

t = 25.6

It will take 25.6 years for the mass of the sample to reach 400 grams.

pav-90 [236]3 years ago
3 0

Answer:

29.6

Step-by-step explanation:

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Step-by-step explanation:

Data

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