PROBLEM $2\mathrm{.}1(20$ Points$)$ The plot shows timeresponse data from a thermal sensor when placed from room temperature $70F$ into a $200F$ water bath.

$($a$)$ Determine the sensor$\text{'}$s static sensitivity and time constant.

$($b$)$ Determine the sensor$\text{'}$s steady$-$state response $y_{ss}(t)$ in volts to the temperature input $70+5sin(3t-0\mathrm{.}1)F.$ If you don't have an answer for part $($a$),$ use static sensitivity $0\mathrm{.}25\frac{V}{}F$ and time constant $0\mathrm{.}1$ s $.$