Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. the speed of each element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half. the half-life of the isotope dubnium-263 is 29 seconds. a sample of dubnium-263 was first measured to have 1024 atoms. after t seconds, there were only 32 atoms of this isotope remaining. write an equation in terms of t that models the situation.

Luke started a weight-loss program. the first week, he lost x pounds. the second week, he lost pounds less than times the pounds he lost the first week. the third week, he lost 1 pound more than of the pounds he lost the first week. liam started a weight-loss program when luke did. the first week, he lost 1 pound less than times the pounds luke lost the first week. the second week, he lost 4 pounds less than times the pounds luke lost the first week. the third week, he lost pound more than times the pounds luke lost the first week.