Question

28. In 1980 the world population was approximately 4.5 billion and in the year 2000 it was approximately 6 billion. Assume that the world population at each time t increases at a rate proportional to the population at time t. Measure t in years after 1980. a) Find the growth constant and give the world population at any time t. b) How long will it take for the world population to reach 9 billion (double the 1980 population)? c) The world population for 2010 was reported to be about 6.9 billion. What population does the formula in (a) predict for year 2010?

b) For the following, (a) locate the centroid of the given region, (b) use Pappus’ Theorem to determine the volume of the solid formed when the region is rotated about the x axis, (c) use Pappus’ Theorem to determine the volume of the solid formed when the region is rotated about the y axis.. The region bounded by: y = x^3 and y =(x)^(1/2) .

Answer 1

a) Let P be the population at any fime t 28 g iren Ne are dP cHt dt K= Consfant (rowth) d P Kclt nfegrating bth fkdt Sides Constant of integration kt+c PctJ C PtJ=et ft= 0 148) At t o P= 4.s billion C. .e 4.S billion e= 4.S billion P(oJ eo kt bilion PitJ= S e 2000 P- 6 billion t-20 Naw osing 2ok P(20)= 4.s e 6 20k 2ok 4.S year kn 6 2o The arowth Constant k 0 0438 year o.o14384 t Plt= . e bilion Population at timet Plt billion finding t when .0l4384t 2 e 9 4.5D l43841t

48-12 year n(2) t * 1980t 48.18 2028 Oo14384 population the population wil double after 4818 years will double .e Jn year 2028 the 6.93 b0lion Paulation in 2010 'P(2010 = 4.sl384 * 3