Mario and Luigi are comparing their daily caloric intake. Each day Luigi chooses healthy 100-calorie snacks such as carrots while Mario chooses to snack on chips and candy that have 200 calories each
Mario (200,400,600)
Luigi (100,200,300)
What does the rate of change for each line represent?
What is Mario's Rate of change? What is Luigi's Rate of change?
How does Mario's rate of change compare to Luigi's Rate of change? Why Are the two rates different from one another?
The rate of change for each line represents how the number of calories consumed increases with each additional snack they eat. In other words, it's the calories per snack for both Mario and Luigi.
To find Mario's rate of change, we look at the sequence of numbers given (200, 400, 600). These numbers represent the total caloric intake after eating 1, 2, and 3 snacks, respectively. To determine the rate of change, we find the difference in calories between successive snacks.
For Mario:
The difference between 400 and 200 is 200.
The difference between 600 and 400 is also 200.
For each snack Mario eats, his caloric intake increases by 200 calories. Therefore, Mario's rate of change is 200 calories per snack.
For Luigi:
Similarly, for Luigi, the numbers given (100, 200, 300) represent the total caloric intake after eating 1, 2, and 3 snacks, respectively.
The difference between 200 and 100 is 100.
The difference between 300 and 200 is also 100.
For each snack Luigi eats, his caloric intake increases by 100 calories. Therefore, Luigi's rate of change is 100 calories per snack.
Comparing their rates of change:
Mario's rate of change (200 calories per snack) is double Luigi's rate of change (100 calories per snack). This is because Mario is snacking on items that are higher in calories. Each of his snacks contributes twice as many calories as Luigi’s healthier snacks.
The two rates are different because the calorie content of the snacks they are choosing is different. Mario's snacks are more calorie-dense, so for each incremental snack he consumes, he's adding more calories compared to Luigi, whose snacks contain fewer calories. This difference in calorie content of their chosen snacks directly translates to the difference in their rates of change regarding caloric intake.