Math Insight

Quiz 2

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Total points: 8
  1. 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.)

  2. 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.

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

  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. 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.