Question

Dorian earns $15 every time he walks a dog. He models the total amount of money he makes walking dogs with the equation f(w)=15w
. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses

0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050

0≤f(w)≤1,050
0 less-than-or-equal-to f left parenthesis w right parenthesis less-than-or-equal-to 1,050

−∞<f(w)≤1,050
negative infinity less than f left parenthesis w right parenthesis less-than-or-equal-to 1,050

0≤f(w)<∞

Answer 1

To determine the appropriate inequality that represents Dorian's earnings based on the information given:

1. Dorian earns $15 for each dog he walks, modeled by the equation \( f(w) = 15w \).
2. \( w \) (the number of dogs) must be a non-negative integer (0 or more), as he cannot walk a negative number of dogs.
3. Assuming there is a maximum earning cap of $1,050, we need to express that Dorian's total earnings fall between $0 and $1,050.

With these considerations, the appropriate inequality representing the range of his earnings is:

**0 ≤ f(w) ≤ 1,050**

Therefore, the answer is:

0 ≤ f(w) ≤ 1,050