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.)

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.

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

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 $a^b$.)

a^b

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.