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I assumed that the initial brightness is $1$, and at death it is $10^{-20}$ (since I can't reach 0 with exponentiation, it will be close enough to 0), and it lived $10^{15}$ years.

Then I solved an equation $x=-\frac{10^{15}}{ln(10^{-20})}$ to get the right results at $10^{15}$ years.

And lastly I made a graph: $y=e^{\frac{-x}{-\frac{10^{15}}{\ln(10^{20})}}}$, that gives me $y=10^{-20}$ at $x=10^{15}$ or a quadrillion years after its creation.

I got $y=0.999$ at $x=13.7\cdot10^{9}$ or 13.7 billion years, or now, which means the white dwarf is 0.999 the brightness it was when it was created during the big bang somehow.

Do these results make sense?

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    $\begingroup$ No they don't. That isn't how WD cooling works and it isn't an exponential decay. I don't understand where you get your 1e-20 at 1e15 years. The faintest white dwarfs are about 1 millionth of a solar luminosity $\endgroup$ – ProfRob Oct 22 '20 at 18:35

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