The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 200 grams of a radioactive isotope, how much will be left after 5 half-lives?

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.