# Carbon dating exponential functions

Express the amount of carbon-14 remaining as a function of time, $$t$$. $\begin A&= A_0e^ \qquad \text\ 0.5A_0&= A_0e^ \qquad \text 0.5A_0 \text f(t)\ 0.5&= e^ \qquad \text A_0\ \ln(0.5)&= 5730k \qquad \text\ k&= \dfrac \qquad \text\ A&= A_0e^ \qquad \text \end$ The function that describes this continuous decay is $$f(t)=A_0e^$$.

We observe that the coefficient of $$t$$, $$\dfrac≈−1.2097×10^$$ is negative, as expected in the case of exponential decay.

To find the half-life of a function describing exponential decay, solve the following equation: $$\dfrac A_0=A_0e^$$ We find that the half-life depends only on the constant $$k$$ and not on the starting quantity $$A_0$$.We may use the exponential decay model when we are calculating half-life, or the time it takes for a substance to exponentially decay to half of its original quantity.We use half-life in applications involving radioactive isotopes.Wiele z tych kobiet to zdesperowane samotne mamuśki i zdradzające żony pragnące nieco zabawy. Czy zgadzasz się zachować tożsamość tych kobiet w tajemnicy?We have already explored some basic applications of exponential and logarithmic functions.

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