Which description is represented by a discrete graph? Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax? The temperature at 9 a.m. was 83° F and is heating up at an average rate of 6°F per hour. What is the temperature x hours later? Juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. What is the total amount of calories he consumed? A bottle contained 2,000 mL of liquid and is being poured out at an average rate of 300 mL per second. How much liquid is left in the bottle after x seconds?
The Correct Answer and Explanation is :
To determine which description is represented by a discrete graph, let’s analyze each scenario presented:
- Kiley’s Purchase: Kiley buys a platter for $19 and bowls for $8 each. The total cost can be expressed as:
[
\text{Total Cost} = 19 + 8b
]
where (b) is the number of bowls bought. This situation is discrete because the number of bowls must be a whole number (0, 1, 2, …). - Temperature Change: The temperature at 9 a.m. is 83°F, increasing at 6°F per hour. The temperature (T) after (x) hours can be expressed as:
[
T = 83 + 6x
]
This scenario represents a continuous graph because (x) can take any value, including fractions and decimals. - Calories Consumed: Juan consumed an egg with 78 calories and cereal with 110 calories per serving. The total calories consumed for (s) servings of cereal can be expressed as:
[
\text{Total Calories} = 78 + 110s
]
This situation is discrete because the servings of cereal must be a whole number. - Liquid in Bottle: A bottle initially containing 2000 mL is poured out at 300 mL per second. The volume left after (x) seconds can be expressed as:
[
\text{Liquid Left} = 2000 – 300x
]
This scenario represents a continuous graph because (x) can take any value, including fractions.
Conclusion: The two scenarios that represent discrete graphs are Kiley’s purchase (the number of bowls is discrete) and Juan’s calorie consumption (the number of servings of cereal is also discrete). Both scenarios involve whole numbers for their respective variables, making their graphs consist of distinct points, while the temperature change and liquid in the bottle are described by continuous variables.
Summary:
- Discrete Graphs: Kiley’s purchase (bowls) and Juan’s calories (servings).
- Continuous Graphs: Temperature change and liquid in the bottle.