Ordinary Differential Equations, Please show all work!
1. Suppose a certain population is given by the function: P(t) = 5(3)^t-1 where t is in days and P(t) is in thousands. The above formula can also be rewritten in the form: P(t) = Ce^kt a) Verify that P(t) = Ce^kt satisfies the IVP P'(t) = kP(t), P(0) = C. b) Find the values of C and k for this particular population. c) Show that this population will double during every time interval of length h = ln(2)/k.