Light from a distant galaxy is detected with a spectral line of frequency fff. In a laboratory on Earth, the same spectral line is measured to have a frequency f0f_0f0. Assuming the galaxy is receding at a non-relativistic speed, the Hubble constant is H0H_0H0, and the speed of light in a vacuum is ccc, which of the following is a correct expression for the look-back time τ\tauτ (the travel time of the light from the galaxy to Earth)?
τ≈f0−fH0f0\tau \approx \frac{f_0 - f}{H_0 f_0}τ≈H0f0f0−f
τ≈fH0(f0−f)\tau \approx \frac{f}{H_0 (f_0 - f)}τ≈H0(f0−f)f
τ≈f0−fH0f\tau \approx \frac{f_0 - f}{H_0 f}τ≈H0ff0−f
τ≈f0H0(f0−f)\tau \approx \frac{f_0}{H_0 (f_0 - f)}τ≈H0(f0−f)f0
