Question

dorian earns $15 every time he walks a dog. he models the total amount of money he makes wallking dogs with the equation f (w) = 15w. which inequlity shows the range of his earnings given the real-world constraints. a. -∞ < f (w) <= 1,050 b. 0 <= f (w) < ∞ c. 0 <= f (w) <= 1,050 d. 0 < f (w) < 1,050 shmunklee answered by shmunk

Answer 1

To determine the appropriate inequality showing the range of Dorian's earnings based on his dog walking equation \( f(w) = 15w \), we need to identify the constraints.

1. **Understanding the parameters:**
- \( f(w) \) represents the total earnings from walking dogs.
- \( w \) represents the number of dogs walked, which cannot be negative (i.e., \( w \geq 0 \)).
- We need to assume a reasonable upper constraint on walking dogs. If we consider that Dorian walks dogs to earn up to a certain limit, let’s say he can potentially earn a maximum of $1,050.

2. **Finding how many dogs he needs to walk to reach $1,050:**
\[
15w \leq 1,050
\]
\[
w \leq \frac{1,050}{15} = 70
\]

So, he can walk up to 70 dogs to earn $1,050.

3. **Determining the inequality for earnings:**
Based on the realistic scenarios, the total earnings \( f(w) \) must be non-negative (since he cannot earn less than $0) and cannot exceed $1,050.

Thus, the correct inequality representing the range of his earnings, given these constraints, would be:

**c. \( 0 \leq f(w) \leq 1,050 \)**.