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Writing and Using Explicit Rules for Arithmetic Sequences

Writing and Using Explicit Rules for Arithmetic Sequences 1.14 - Solution

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a
First, let's write the ordered pairs using the numbers we are given. The first number, represents the weight of the box as one item is taken out of it. Thus, the ordered pair is We can write the rest of them in a similar manner. Let's now use the slope-intercept form of the equation to write the function. We can calculate the slope by substituting two arbitrary points from above into the Slope Formula. Let's use and
Simplify
Thus, the slope is Now we can find by substituting the slope and a point, let's use into the equation.
Simplify
Now we can write the function.
b

We know the weights of the box after taking out each item. Hence, if we calculate the differences between consecutive weights, we will know the weight of each item. The weight of each yearbook is ounces.

c

It is given that the weight of the box when full is ounces, and when it's empty is ounces. Therefore, by subtracting from we can calculate the weight of all of the items, not including the weight of the box. Now if we divide this weight by the weight of book, we will know how many items were in the box. There were items in the box.