Veronica sells berries at a farmer's market. She pays $45 for the booth, and earns $5 per pound of berries sold. She sells between 10 and 30 pounds of berries at each market. The function p(b)=5b−45 represents Veronica's market earnings as a function of pounds of berries sold. What is the practical domain of the function? Please help! Thank you.

Veronica typically sells a maximum of 30 pounds of berries but could also sell 10 pounds in the least. Therefore, the PRACTICAL DOMAIN would be between 10 and 30 pounds of berries. This can be expressed in terms of an inequality: 10 ≤ b ≤ 30 (i.e. all integers between 10 and 30 inclusive).   If we were to be asked for the THEORETICAL DOMAIN for the same function p(b)=5b−45. We would be considering the set of logical values of b that would generate a reasonable output for the function. Clearly, we could plausibly put any value of b in the function and still get a reasonable output.  So the theoretical domain of the function p(b)=5b−45  is the set of all real numbers.