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Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

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Question:

A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.

- How many boxes were in stock when they opened?

- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.

- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer:

1.
Initial = 244

2.
b = 244 + 52h

3. 660 boxes

Explanation:

Given


Rate = 52\ per\ hour


Total\ boxes\ in\ 3\ hours = 400

Solving (a): Initial Number of boxes

First, we calculate the number of boxes made in 3 hours


Boxes = Rate * Hours


Boxes = 52 * 3


Boxes = 156

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:


Initial = 400 - 156


Initial = 244

Solving (b): Linear function


b = boxes


h = hours

Since, we have the rate and the initial number of boxes.

The linear function is:


Boxes = Initial + Rate * Hours

i.e.


b = 244 + 52 * h


b = 244 + 52h

Solving (c): Boxes at the end of the 8th hour

We have:


b = 244 + 52h

In this case:


h = 8

Substitute 8 for h


b = 244 + 52 * 8


b = 244 + 416


b = 660

Hence, there are 660 boxes at the end of the 8th hour

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