$($a$)$ If $P$ is the point $(15,1,470)$ on the graph of $V,$ find the slopes of the secant lines $PQ$ when $Q$ is the point on the graph with $t=5,10,20,25,$ and $30.$

Slopes of secant lines passing through $P(15,1,470)$ and $Q(t,V(t))$ can be calculated using the following.

$m_{sec}=\frac{V(t)-1,470}{t-15}$

We begin by calculating the slope when $t=5.($In the last step, round your answer to one decimal place.$)$

$m_{sec}=\frac{V(5)-1,470}{5-15}$

$=-,-1,470$

$=$

A tank holds $6,000$ gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume $V$ of water remaining in the tank $($in gallons$)$ after minutes.

$\backslash$table$[[t($min$),5,10,15,20,25,30],[v($gal$),4,086,2,634,1,470,630,156,0]]$

$($a$)$ If $P$ is the point $(15,1,470)$ on the graph of $V,$ find the slopes of the secant lines $PQ$ when $Q$ is the point on the graph with $t=5,10,20,25,$ and $30.$

$($b$)$ Estimate the slope of the tangent line at $P$ by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to $P.$

$($a$)$ If $P$ is the point $(15,1,470)$ on the graph of $V,$ find the slopes of the secant lines $PQ$ when $Q$ is the point on the graph with $t=5,10,20,25,$ and $30.$

Slopes of secant lines passing through $P(15,1,470)$ and $Q(t,V(t))$ can be calculated using the following.

$m_{sec}=\frac{V(t)-1,470}{t-15}$

We begin by calculating the slope when $t=5.($In the last step, round your answer to one decimal place.$)$

$m_{sec}=\frac{v(5)-1,470}{5-15}$

$=\frac{-1,470}{?}$