Asphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is h inches above the first plane. the resulting portion of the sphere between the two planes is called a spherical segment; see the picture: in math 125, you will show that the volume v of the spherical segment is given by this formula (which we will assume): v = (π/3)h(27 – h2). give exact answers to the questions below. (a) find the volume of the spherical segment if h=1: (b) find the rate of change of the volume with respect to h of the spherical segment at h=1: (c) use the tangent line approximation at h=1 to estimate the value of h that will yield a spherical segment having volume 25 cubic inches:

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?