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.

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.

1.

2.

3. 660 boxes

Step-by-step explanation:

Given

Solving (a): Initial Number of boxes

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

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:

Solving (b): Linear function

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

The linear function is:

i.e.

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

We have:

In this case:

Substitute 8 for h

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