Determine the ratio between h and the amount of juice in the pitcher.
See solution.
Practice makes perfect
We have been given that the height h of the juice in the pitcher is a function of the amount of the juice j that has been poured out. We are asked to write a function rule that represents this situation and to determine h after 47 oz have been poured out. We will follow two-step plan.
h When Half the Juice Is Poured Out
We have 64 oz of juice in the pitcher at the beginning, and the height of the juice is 10 inches. When we pour out half of the juice, the height also decreases by half.
ccc
64 oz & ⇒ 64/2 oz & ⇒ 32 oz [0.9em]
10 in. & ⇒ 10/2 in. & ⇒ 5 in.The new height of the juice becomes 5 inches.
Value of j to Decrease h by 1
In the previous part, we saw that pouring out half of the juice also decreases the height by half. Therefore, if we want to decrease the height 1 inch, which is 110 of the beginning height, we need to pour out 110 of the juice. We started with 64 oz of juice.
110 of the juice is equal to 6.4 oz. This means that, for each 6.4 oz decrease in the amount of juice, the height decreases by 1 inch. Therefore, we can write the function rule for the height as follows.
h= 10 - j/6.4
h When j=47
To find the height of the juice after 47 oz have been poured out, we will substitute this value for j into our rule and solve for the height.
