Let the function x be dened by x(t) = a ebt, where thas units of seconds and x has units of meters. (for b< 0, this could be a fairly accurate model of the motion of a bullet shot into a tank of oil.) show that the taylor series of this function makes sense if and only if a and b have certain units. instruction. 1. write down the taylor series of the function x(t) 2. use the dimensional analysis to determine the units of a and b. the earth's surface is about 70% water. mars's diameter is about half the earth's, but it has no surface water. compare the land areas of the two planets. instruction 1. draw diagrams of earth and mars 2. label physical quantities using variables. 3. solve this problem using only the information given in the problem.