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The weight of a radioactive isotope was 96 grams at the start of an experiment. after one hour, the weight of the isotope was half of its initial weight. after two hours, the weight of the isotope was half of its weight the previous hour. if this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time? a. graph w b. graph x c. graph y d. graph z

Chosen according to the volume of oil it can haul, as shown in at a railway yard, locomotives are used to haul containers carrying the table. locomotive capacity a450 0 -750 cubic feet cg35 750-1,500 cubic feet br73 1,500-2,500 cubic feet yh61 2,500-3,500 cubic feet & the four cylindrical containers listed in the table need to be hauled. cylinder length (ft.) diameter (ft.) fill level a 40 , 12 half b 24 8 full c 16 16 full 6 12 full d match each container to the locomotive needed to haulit a450 cylinder a yh61 cylinder d

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?