QuestionAn organism has $20 \mathrm{~g}$ of carbon-14. After 11,400 years (2 half-lives), how much remains? a) 0 g b) 2.5 g c) 5 g d) 10 g

Studdy Solution

STEP 1

Assumptions1. The initial amount of carbon-14 is20g. . The half-life of carbon-14 is5700 years.
3. We want to know the amount of carbon-14 remaining after11400 years.

STEP 2

The decay of a substance like carbon-14 can be modeled by the exponential decay formula $= N0 \times \left(\frac{1}{2}\right)^{\frac{t}{}}$ where- is the final amount of the substance- $0$ is the initial amount of the substance- $t$ is the time that has passed- is the half-life of the substance

STEP 3

We can plug in the given values for the initial amount of carbon-14 ( $0$ ), the time that has passed ( $t$ ), and the half-life of carbon-14 ($$) into the formula.
$=20g \times \left(\frac{1}{2}\right)^{\frac{11400}{5700}}$

STEP 4

implify the exponent in the formula.
$=20g \times \left(\frac{1}{2}\right)^{2}$

STEP 5

Calculate the final amount of carbon-14 ($$).
$=20g \times \left(\frac{1}{4}\right) =5g$ The amount of carbon-14 that remains after11,400 years is approximately5g.

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