Math Insight

Quiz 2

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Total points: 8
  1. Consider the dynamical system below: \[ \left\{ \begin{array}{r c l} \epsilon_{ n+1} & = & 0.8 \epsilon_n \\ \epsilon_0 & = & 59 \\ \end{array} \right. \]

    Calculate the time at which the state variable reaches 32.45. Enter your solution in the box below, accurate to at least four significant digits.


  2. Find the half life for the system below \[ \left\{ \begin{array}{r c l} \nu_{ t+1} - \nu_t & = & -0.8 \nu_t \\ \nu_0 & = & 38 \\ \end{array} \right. \]

    The half life is

    (Keep at least four significant digits in your answer.)

  3. Compute the solution to the discrete dynamical system \[ \left\{ \begin{array}{r c l} w_{ n+1} & = & \frac{1}{ 3 } w_n \\ w_0 & = & 40\\ \end{array} \right. \]

    $w_n = $
    (To enter an exponent use the “^” character. For example, enter a^b for $a^b$.)

  4. Rewrite the discrete dynamical system \begin{align*} s_{ n +1} - s_{ n } &= c s_{ n } \\ s_{0} &= 8.8 \end{align*} in function iteration form.

    $s_{ n +1} = ($
    $) \, s_{ n }$