Cooper Section $8\mathrm{.}5$ #$3$

The volume $of$ water $in$ a reservoir depends $on$ the height $of$ the water measured $on$ a marker $on$ a dam. $If$

the volume $isV(x)$ gallons when the height $isx$ meters:

$a.$ What are the units $of{V}^{\text{'}}(x)?$

$A.$ gallons per meter

$B.$ gallon$-$meters

$C.$ gallons per minute

$D.$ meters per gallon

$b.$ What $is$ the meaning $of{V}^{\text{'}}(30)=5*{10}^7?$

$A.$ The volume increases $by30$ gallons whenever the height $is$ increased $by$ one meter.

$B.$ The volume increases $by5*{10}^7$ gallons whenever the height $is$ increased $by$ one meter.

$C.$ The volume increases $by5*{10}^7$ gallons whenever the height $is$ increased $by30$ meters.

$D.$ The volume increases $by30$ gallons whenever the height $is$ increased $by5*{10}^7$ meters.

$E.$ When the height $is30$ meters, the volume $is$ increasing $at$ a rate $of5*{10}^7$ gallons per $30$

meters $of$ height.

$F.$ When the height $is30$ meters, the volume $is$ increasing $at$ a rate $of5*{10}^7$ gallons per meter $of$

height.

$G.$ When the height $is5*{10}^7$ meters, the volume $is$ increasing $at$ a rate $of30$ gallons per meter $of$

height.