Select Function $1,$

T$($t$)=50$e$0\mathrm{.}5$t$,$

under the Explore & Test section of the Explore It$.$

$($a$)$

A scientist wants to know the temperature of a solution at $5$ seconds. Set the t$-$coordinate of the fixed point to $5.$ What is the temperature at $5$ seconds to one decimal place?

$$C

$($b$)$

The scientist wants to use the secant line to estimate the cooling rate after $5$ seconds. Drag the adjustable point to time $6.$ What is the rise over run of the secant line? $($Round your answer to one decimal place.$)$

$$C$/$min

$($c$)$

Now drag the adjustable point to time $5\mathrm{.}5.$ What is the rise over run? $($Round your answer to one decimal place.$)$

$$C$/$min

$($d$)$

What is the slope of the secant line in part $($c$)$ to one decimal place?

$$C$/$min

$($e$)$

Continue to move the adjustable point toward the fixed point until the secant and tangent lines overlap. What is the slope of the tangent line to one decimal place $($the instantaneous cooling rate$)?$

$$C$/$min