Environmental scientists are monitoring a 75 cm3 water sample collected from a geothermal hot spring to estimate the population of the thermophilic archaeon Sulfolobus acidocaldarius. They performed the following serial dilutions:
The scientists transferred 0.15 cm3 of Solution 3 onto a nutrient agar plate. After incubation under aerobic conditions at 75∘C75^\circ\text{C}75∘C, 53 distinct colonies grew on the plate.
Calculate the estimated total number of archaeal cells in the original 75 cm3 sample.
Express your answer in standard form to three significant figures. Show your working.