Let's solve the problem step-by-step:
1. Understanding the Problem:
- Diep starts with a loaf of bread that is 65 centimeters long.
- Each day, Diep cuts 15 centimeters from the loaf for his sandwich.
- We need to determine the length of the bread, [tex]\(I\)[/tex], after [tex]\(d\)[/tex] days.
2. Finding the Equation:
- Initially, the loaf is 65 centimeters.
- Every day [tex]\(d\)[/tex], 15 centimeters are cut, so the length decreases by 15 centimeters each day.
- On the first day [tex]\( (d=1) \)[/tex], the length of the bread will be [tex]\( 65 - 15 \times 1 \)[/tex].
- On the second day [tex]\( (d=2) \)[/tex], it will be [tex]\( 65 - 15 \times 2 \)[/tex], and so on.
Thus, the general equation for the length of the bread after [tex]\( d \)[/tex] days is:
[tex]\[
I = 65 - 15d
\][/tex]
3. Graph Type:
- Since the bread is cut in whole centimeters each day, the number of days ([tex]\(d\)[/tex]) and the corresponding lengths are discrete values.
- You would not have a situation where you cut a fractional number of centimeters per day.
Given this explanation, the correct equation is:
[tex]\[
I = 65 - 15d
\][/tex]
And the graph of this equation is discrete since we only consider whole days and whole centimeters.
So the correct answer is:
[tex]\[
I = 65 - 15d; \text{discrete}
\][/tex]
