Esta calculadora calculará la vida media, la cantidad inicial, la cantidad restante y el tiempo, con los pasos que se muestran.

There are units of mass of a substance with a half-life of units of time. In units of time, there will remain units of mass of the substance.

Enter any three values.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Solution

Your input: find $N(t)$ in $N(t)=N_0e^{-kt}$ given $N_0=250$, $t_h=15$, $t=100$.

$N(t)$ is the amount after the time $t$, $N_0$ is the initial amount, $t_h$ is the half-life.

First, find the constant $k$.

We know that after half-life there will be twice less the initial quantity: $N\left(t_h\right)=\frac{N_0}{2}=N_0e^{-k t_h}$.

Simplifying gives $\frac{1}{2}=e^{-k t_h}$ or $k=-\frac{\ln\left(\frac{1}{2}\right)}{t_h}$.

Plugging this into the initial equation, we obtain that $N(t)=N_0e^{\frac{\ln\left(\frac{1}{2}\right)}{t_h}t}$ or $N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_h}}$.

Finally, just plug in the given values and find the unknown one.

From $N(t)=250\left(\frac{1}{2}\right)^{\frac{100}{15}}$, we have that $N(t)=\frac{125 \sqrt[3]{2}}{64}$.

Answer: $N(t)=\frac{125 \sqrt[3]{2}}{64}\approx 2.46078330057592$.