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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