Answer
${\bf1.01\times 10^{23}}\;\rm electron$
Work Step by Step
To find the number of electrons, we first need to find the total amount of charge.
We know that the current is given by
$$I=\frac{dQ}{dt}$$
Thus,
$$dQ=Idt$$
Taking the integral,
$$\int_0^QdQ=\int_0^\infty Idt$$
Plug $I$ from the given formula, (we use the SI system only here so we had to convert from hours to seconds);
$$ Q=\int_0^\infty \left(0.75 \;e^{-t/21600}\right)dt$$
$$ Q=0.75 \left(\dfrac{1}{-1/21600}\;e^{-t/21600}\right)_0^\infty$$
$$ Q=-16200 \left( e^{-\infty/21600}-e^0\right) $$
$$Q=\bf16200\;\rm C$$
Recalling that $Q=Ne$, so
$$N=\dfrac{Q}{e}=\dfrac{16200}{1.6\times 10^{-19}}$$
$$N=\color{red}{\bf1.01\times 10^{23}}\;\rm electron$$
