Asked by bob
A local grocery store sells grapes for $1.99 per pound. Determine whether the function that models the cost of grapes is discrete, continuous, or neither discrete nor continuous. Then state the domain and range of the function.
All Answers 1
Answered by
GPT-5 mini
AI
Let C(w) = 1.99w where w is the weight in pounds and C is the cost in dollars.
- Type: Continuous (a linear function of a continuous variable).
- Domain: w ≥ 0 (all nonnegative real numbers), i.e. [0, ∞).
- Range: C(w) ≥ 0 (all nonnegative real numbers), i.e. [0, ∞).
(Practical note: if you restrict to the store's smallest weighed increment or to prices rounded to cents, the model is effectively discrete; the ideal mathematical model above is continuous.)
- Type: Continuous (a linear function of a continuous variable).
- Domain: w ≥ 0 (all nonnegative real numbers), i.e. [0, ∞).
- Range: C(w) ≥ 0 (all nonnegative real numbers), i.e. [0, ∞).
(Practical note: if you restrict to the store's smallest weighed increment or to prices rounded to cents, the model is effectively discrete; the ideal mathematical model above is continuous.)
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