The number of zombies is growing proportionally to the number of zombies present. At time 0, 25 people were infected. After 10 days since the first infections, 10000 people had been infected. (Relevant section: 1.1) Mathematica Tasks: 1. Since we know the number of zombies is growing proportionally to the number of zombies present, we can construct a differential equation which models the number of zombies P(t): dP dt = kP. Specify the initial condition(s) of the differential equation. 2. From Example 5 in section 1.1, we learn that the general solution of the above differential equation takes form P(t) = Cekt. Use the following Mathematica command to define a function: P[t ] = C ∗ Eˆ(k ∗ t), and check the value of P(t) at t = 0, 1, 20 (days) by putting in P[0], P[1] and P[20]. 3. Verify P(t) we defined above is the general solution of the differential equation in Problem 1 by plugging P(t) into the differential equation: Simplify[P 0 [t] − k ∗ P[t]]. The Simplify function asks Mathematica to simplify the expression. Based on the result of the command, do you think P(t) is the general solution? 4. Use Solve and the initial conditions to find the unknown consta