You can now apply the initial condition x(0) = No. combine logarithms, and finally exponentiale to solve Eq. (4) for the particular solution 130 (5 100 - to + For7100 of Eq. (2). The slope field and solution curves shown in Fig. 1.4.15 suggest that, whatever is the initial value co. the solution x (r ) approaches 100 as / - too. Can you use Eq. (5) to verify this conjecture? FIGURE 14.1S. Shoppe lick mad INVESTIGATION: For your own personal logistic equation, take a = ify and edution garves lot b = 1 in Eq. (1). with on and a being the largest two distinct digits (in either order) in your student ID number. (a) First generate a slope field for your differential equation and include a sufficient number of solution curves that you can see what happens to the population as -+ + co. State your inference plainly. (b) Next use a computer algebra system to solve the differential equation symboli- cally; then use the symbolic solution to find the limit of x(f) as r -> too. Was your graphically-based inference correct? (c) Finally. stale and solve a numerical problem using the symbolic solution. For instance. how long does it take x to grow from a selected initial value x to a given target value x