To determine the age of the sample collected by the space station astronauts, NASA scientists used a dating method similar to carbon-14: rubidium-strontium dating. This method consists in measuring the respective quantities of rubidium 87, strontium 87 and strontium 6 in the sample to be dated. The various ratios of these measures make it possible to bring out an indicator called the guiding coefficient. It is this indicator that makes it possible to determine the age of the specimen studied. Indeed, one can associate the time t elapsed since the formation of the rock (in billions of years) with the directing coefficient A thanks to the following equation. 0.1474t A = e 1 a) Knowing that the guiding coefficient A of the asteroid fragment was 0.45, calculate his age. b) Knowing that the asteroid fragment was covered with dust whose director coefficient A was 0.95, determine the age of this dust.