The number of Gilmore Girls fans is modeled by a Logistic Growth IVP model given by dG = kG ( 1 dt G(0) = Go M where M and k are fixed parameters, t is measured in years and G is measured in millions (for example, since the world population in the release year of 2000 was 6083 million people then Go = 6083). The general solution to the model is G(t) = 1+ Ce-kt where C is an unknown constant. (a) Verify that this is a general solution to the differential equation. M Hint: It will be useful to use the fact that Ce-kt -1 after differentiating. G (b) Use the initial condition to solve for the particular solution with C in terms of the parameters k, M, and Go and state the interval of validity (interval of the solution). Note: Do not use Go = 6083. That was a joke. Keep it as a general fixed constant Go. (c) Assuming humanity lasts indefinitely, what population value will the Gilmore Girls fanbase tend to? Note: Do not wse any techniques from section 2.1 with phase portraits. Instead investigate the solution. (d) Assuming now that Go = 6, 083, M = 24, 000 and that after 12 years the fanbase doubles. Determine the parameter k. Leave your answer exact.