Step 1 :The demand and price for a certain model of a youth wristwatch are related by the equation \(p=D(q)=28-2.25 q\), where \(p\) is the price (in dollars) and \(q\) is the quantity demanded (in hundreds).
Step 2 :To find the price when the demand is 0 watches, we substitute \(q=0\) into the equation. This gives us \(p=D(0)=28-2.25*0=28\). So, the price when the demand is 0 watches is \$28.
Step 3 :To find the price when the demand is 400 watches, we substitute \(q=4\) into the equation (since \(q\) is in hundreds). This gives us \(p=D(4)=28-2.25*4=19\). So, the price when the demand is 400 watches is \$19.
Step 4 :To find the quantity demanded for the watch when the price is \$10, we rearrange the equation to solve for \(q\) when \(p=10\). This gives us \(q=(28-10)/2.25=8\). Since \(q\) is in hundreds, the quantity demanded for the watch when the price is \$10 is \(8*100=800\) watches.
Step 5 :Final Answer: The quantity demanded for the watch when the price is \$10 is \(\boxed{800}\) watches.