= Solution
At height $z$ above the free lower end, a uniform vertical filament carries the weight of length $z$. With cross-sectional area $A$,
$$
F(z)=\rho A g z,\qquad\sigma(z)=\rho g z,
\qquad\boxed{\sigma_{\max}=\rho g L.}
$$
\b[The maximum <stress> is at the top and is independent of diameter.] The diameter cancels because both <mass> and load-bearing area scale with $A$. Neglecting self-heating gradients, evaporation and initial fabrication <stress>, this top point sets the first creep-strain limit.
For a clearly labelled external reference estimate, take $\rho=1.93\times10^4\,\mathrm{kg\,m^{-3}}$. Then $\sigma_{\max}=1.89\times10^4\,\mathrm{Pa}=0.0189\,\mathrm{MPa}$; the area is $3.14\times10^{-8}\,\mathrm{m^2}$ and the total suspended <mass> is about $6.06\times10^{-5}\,\mathrm{kg}$. The <density> is independently tabulated, not invented as a supplied 2016 value.<Atomic and nuclear properties of tungsten by the Particle Data Group>[2009 table, density entry]{ref}
Use the original map's top <temperature> axis at $2500^\circ\mathrm C$ and its \b[right-hand tensile-stress axis], so no uncertain shear-stress conversion or additional <shear modulus> is required. The point lies in C, between the $10^{-9}$ and $10^{-8}\,\mathrm{s^{-1}}$ contours, nearer $10^{-8}$. A logarithmic interpolation of the scanned contours gives about $6\times10^{-9}\,\mathrm{s^{-1}}$, with only graphical precision. Thus
$$
t_f\simeq\frac{0.05}{\dot\varepsilon_{\max}}
\simeq8\times10^6\,\mathrm s
\simeq2.3\times10^3\,\mathrm h,
$$
or \b[of order three months in this steady-rate, reference-density map estimate]. Reading only the bracketing contours gives the appropriately broad interval $5\times10^6$ to $5\times10^7\,\mathrm s$; the graph does not support an exact service-life number.
For the exact prescribed input, the answer remains
$$
\boxed{t_f\simeq\frac{0.05}{\dot\varepsilon(2500^\circ\mathrm C,\rho gL)}}.
$$
This estimate uses the cited reference <density> and the grain-size assumptions of the supplied map. <Thermal expansion> lowers <density>, and an evolved area or tertiary <material creep> changes the rate; a steady initial-rate estimate is not a guaranteed lifetime. In particular, a different filament <grain size> could require a different map. Other failure mechanisms could shorten useful life.
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