To answer these questions, we need to analyze the relationship between the time elapsed and the number of flyers Chris has. We can use the given table data to determine this relationship.
First, let’s summarize the data provided:
- At 10 minutes, Chris has 98 flyers.
- At 15 minutes, Chris has 133 flyers.
- At 20 minutes, Chris has 168 flyers.
- At 25 minutes, Chris has 203 flyers.
From this data, we can determine two key pieces of information:
(a) The number of flyers Chris already had when he started printing (initial count at time 0).
(b) The rate at which the number of flyers Chris has is changing (slope of the relationship).
### Step-by-Step Solution
To determine these values, let's apply a method known as linear regression to see how the number of flyers changes over time.
#### Part (a) Initial Number of Flyers
The initial number of flyers is represented by the y-intercept in a linear regression model. This value tells us how many flyers Chris started with before the printing process began. For this data:
Number of flyers Chris already had:
[tex]\[
\text{Initial flyers} = 28.0 \text{ flyers}
\][/tex]
#### Part (b) Rate of Change
To find the rate at which the number of flyers Chris has is changing, we look at the slope of the linear relationship. This slope represents the rate per minute.
Rate at which the number of flyers Chris has is increasing:
[tex]\[
\text{Rate of increase} = 7.0 \text{ flyers per minute}
\][/tex]
### Conclusion
(a) How many flyers did Chris already have when he started printing?
[tex]\[
\boxed{28} \text{ flyers}
\][/tex]
(b) Choose the statement that best describes how the time and the number of flyers Chris has are related.
As time increases, the number of flyers Chris has increases.
At what rate is the number of flyers Chris has increasing?
[tex]\[
\boxed{7} \text{ flyers per minute}
\][/tex]
Thus, with each passing minute, Chris prints an additional 7 flyers, and he started with 28 flyers initially before the printing began.
