Please include what needs to be plugged in Excel

d 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Name 40 35 30 25 20 15 10 5 t time 0.061 0.12 0.18 0.24 0.3 0.36 0.42 Numerical Solution to Euler Method 2 y (approx) ldt = Click to Enter Data f(t,y) Exact solution (if known) Initial Conditions Initial time Final time Initial y value Approximation Data # of subintervals Click for Info estimate the value ot the steady state solution obtained in exercise ywith the pure logistic and K = 300? Does the answer make sense? b) Use qualitative methods to find an exact expression for the steady state solution that you estimated in a). (Hint: You should obtain a quadratic equation in the variable u = . ) 11. Using the file ode.xls, numerically solve the logistic differential equation for the U.S. population growth from 1790 to 1940 using the values r =.0315 and K = 189 with No = 3.929. (We are assuming that t = 0 corresponds to 1790.) Compare the population 1940 with the actual census figures given in the data estimates for the years 1800, 1810, . file us_pop.xls. 05 3 2 50 yexact 12. a) b) c) yapprox 2.000 2.120 2.247 2.382 2.525 2.676 2.837 3.007 3.188 Type Comments Here y approx 2.000 2.120 2.247 2.382 2.525 2.676 2.837 3.007 3.188 The logistic differential equation($j can actually be solved explicitly using separation of variables. Verify that for any constant C formula (5.8) below gives a solution. (5.8) 1+cert Show that if No = N(O) then the value of C in (5.8) is given by -1. In our discussion of the logistic we showed that when the population starts out below its carrying capacity the rate of increase of the population reaches a maximum when the 79