Question

part a
which situation could be modeled by a function with a domain of all positive integers?

a the distance a runner has moved during a race as a function of time since the race started

b the amount of fish food required in a fish tank as a function of the number of fish in the tank

c the amount of power required to operate a computer as a function of the length of time the computer is on

d the amount of water required by an animal as a function of the mass of the animal

Explanation:

Step1: Analyze Option a

Time since race started can be any non - negative real number (e.g., 1.5 seconds), not just positive integers. So the domain here is not all positive integers.

Step2: Analyze Option b

The number of fish in a tank is a positive integer (you can't have a fraction of a fish). The amount of fish food required depends on the number of fish (a positive integer). So the domain of the function (number of fish) is all positive integers.

Step3: Analyze Option c

The length of time the computer is on can be any non - negative real number (e.g., 2.3 hours), not just positive integers. So the domain is not all positive integers.

Step4: Analyze Option d

The mass of an animal can be any positive real number (e.g., 1.2 kg), not just positive integers. So the domain is not all positive integers.

Answer:

b. the amount of fish food required in a fish tank as a function of the number of fish in the tank