Mathematics for Natural Science

Question

Suppose a radioactive substance decays according to the equation $y=2000e^{-0.75t}$, where $y$ represent the mass in grams after $t$  hours.
How much of $2$ milligram will remain after $8100$ years?

Comments

The given equation shows the exponential decay of a radioactive substance.

In general, we can write the equation as $N= N_0 e^{-\lambda t}$ where $t$ represents the time, $\lambda$ is decay constant,  $N_0$ is the initial quantity of the radioactive substance at $t=0$ and $N$ is the remaining quantity after time $t.$

So, here, initial quantity is given as $N_0 = 2 \ mg =2 \times 10^{-3} g,$

$\lambda= 0.75$ (Taking it from the given equation because it is not given specifically) and $t= 8100 \ years = 8100 \times 365 \times 24 \ hours$

(Assuming every year has 365 days and each day has 24 hours)

So, remaining quantity (N) $= 2 \times 10^{-3} e^{-0.75\times  8100 \times 365 \times 24 } $ grams

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Tnks alot