Math Snap

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.
$$=20g \times \left(\frac{1}{2}\right)^{2}$$

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.