Happy Quiz
(counts only if it helps you)

1. A deterministic dynamical system (or process) that exhibits extreme sensitivity to initial conditions is said to be ________________ . Is such behavior random? _______ Why or why not? _________________________

2. A mass M of radioactive material decays at a rate proportional to the amount present at time t.

(a) Write the general differential equation that expresses this fact.

(b) Suppose that the half-life of this substance is 4.2 days. In other words, if M = 8 kg at time t = 0, then M = ____ kg at time t = 4.2. Solve the particular equation for this example of radioactive decay.

(c) Using the window [0, 10] ´ [0, 10], sketch the slope field for the general solution before the constant of integration is known. Then overlay your solution in part (b) onto this slope field.

(d) Using Euler’s method with a step size of 0.5 days, and using only the initial condition M(0) = 8, develop an estimate for the mass present at time t = 1.5 days. How close is this to the true value? Show all of your work.