Math Problem Statement
Solution
The question asks to select the most appropriate domain for the profit function of a bakery, given by the equation , where represents the number of pastries sold per day. The domain should represent realistic values for .
Here are the options to evaluate:
- is an integer, such that : This is practical as you can't sell a fractional pastry and sales cannot be negative.
- is a rational number: This allows for fractional pastries, which isn't realistic.
- : This includes negative numbers, which aren't viable for the number of pastries sold.
- is a real number, such that : This includes all non-negative real numbers, which is not practical because it allows for fractional pastries.
- is an irrational number: This option is not practical since selling an irrational number of pastries is not possible.
The best choice here is:
- is an integer, such that , as it best fits the realistic scenario of counting whole pastries.
Would you like further details on how this function works or have other questions about the topic?
Here are five additional related questions you might find interesting:
- What is the maximum profit the bakery can achieve according to the function ?
- How many pastries must the bakery sell to achieve maximum profit?
- How does the shape of the parabola relate to the bakery's profits?
- Can the profit ever become negative according to this model? Under what circumstances?
- How would the profit function change if the bakery's base cost per pastry or sale price were to change?
Tip: Always check the practical implications of mathematical models in real-life scenarios to ensure they reflect possible and logical outcomes.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Domain of a Function
Formulas
p(x) = -0.2(x - 60)^2 + 150
Theorems
Quadratic Function Properties
Domain and Range Theorems
Suitable Grade Level
Grades 8-10
Related Recommendation
Maximizing Profit with a Quadratic Function: P(x) = −2x² + 50x − 200
Find Profit and Loss Intervals for the Quadratic Function P(x) = −2x^2 + 402x − 4180
Profit Function P(x) = -0.75x^2 + 6x - 9: Determine Profitable Units
Average Rate of Change of a Quadratic Profit Function from x = 3 to x = 5
Maximum Profit and Break-Even Points of Quadratic Function