Consider these actual data for three Cepheids in the galaxy M$100$; the luminosities were determined with Leavitt's law from the observed periods $($measured with observations from the Hubble Space Telescope$).$

Cepheid $1$ : luminosity $=3\mathrm{.}9{10}^{30}W,$

apparent brightness $=9\mathrm{.}3{10}^{-19}\frac{W}{m^2}.$

Cepheid $2$: luminosity $=1\mathrm{.}2{10}^{30}W,$

apparent brightness $=3\mathrm{.}8{10}^{-19}\frac{W}{m^2}$

Cepheid $3$ : luminosity $=2\mathrm{.}5{10}^{30}W,$

apparent brightness $=8\mathrm{.}7{10}^{-19}\frac{W}{m^2}$