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. Write an equation to represent the number of biscuits left in the box in slope intercept form of the time, in days. Be sure to define your variables.
identify the domain and range for this function
Let's define:
- t as the time in days
- N as the number of biscuits left in the box
Since Anchor always gets three biscuits a day, we can deduce that initially, Bryan had 3 biscuits for each of the 10 days before the count was made. So, at t = 0, there were:
N0 = 3 biscuits/day * 10 days = 30 biscuits
To find the equation in slope-intercept form, we need to determine the slope and y-intercept. The slope represents the rate of change, which in this case would be -3 biscuits per day since the number of biscuits decreases by 3 each day. The y-intercept is the initial number of biscuits, which is N0.
Therefore, the equation in slope-intercept form is:
N = -3t + N0
The domain for this function is all real numbers since time can take any value. The range is all non-negative integers as the number of biscuits cannot be negative, and it can range from 0 (if all biscuits are already consumed) to a maximum of 106 biscuits (as stated in the problem).