Question

1. Bryan bought a box of biscuits for his dog, Anchor. Anchor always gets three biscuits a

day. At the start of the tenth day after opening the box, Bryan counts 106 biscuits left in
the box.
1A. Write an equation to represent the number of biscuits left in the box as a function of the time, in days. Be sure to define your variables.
Answer: _____

2. Identify the slope and the y-intercept of this function, and explain the meaning of each
value in this situation:

3. Identify the domain and the range of this function.
Domain: ____
Range: _____

Answer 1

1. The equation to represent the number of biscuits left in the box as a function of time, in days, is:

Let x be the number of days since Bryan opened the box.

Then, the number of biscuits left in the box is 3x + 106.

This equation states that on the first day, there were 106 biscuits left in the box (106 is the y-intercept). As each day passes, the number of biscuits left in the box increases by 3 (the slope).

2. The slope of the function is 3, which means that the number of biscuits left in the box increases by 3 each day. The y-intercept is 106, which represents the initial number of biscuits left in the box on the first day.

3. The domain of the function is the set of all real numbers (since time is measured in days, and days are a continuous variable). The range of the function is the set of all integers greater than or equal to 106 (since the number of biscuits left in the box is always an integer).

Explanation: