Suppose an experiment is designed to test the durability of batteries in different conditions. all of the batteries tested are double-a (aa) brand x. all sets of batteries are preconditioned in different environmental conditions for exactly 168 hours (1 week).
set 1: 0°c (freezing point of water)
set 2: 24°c (approximately room temperature)
set 3: 37°c (approximately body temperature)
the batteries are then continuously used to power identical mechanical drummer toys. as long as the toy keeps drumming the battery is considered functional. the drumming time for each toy is measured as an indication of battery durability.
in this experiment, which condition is not controlled?
brand of batteries
type of battery (battery size)
temperature
test for durability

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?