Q:

# The function f(x)=70n -400 models the profit of the instructor of a guitar class per month, where n is the number of students enrolled in the class. How many students must be enrolled in the class for the instructor to make a profit? How many students must be enrolled in the class if the instructor needs to make 1,000.00 profit per month?

Accepted Solution

A:
Answer:At least 6 students must be enrolled in the class for the instructor to make a profit.At least 20 students must be enrolled in the class for the instructor to make $1,000 (or more) profit per month.Step-by-step explanation:The function $$f(x)=70n -400$$ models the profit of the instructor of a guitar class per month.1. If the instructor makes a profit, then$$f(x)>0\\ \\70n-400>0\\ \\7n-40>0\\ \\7n>40\\ \\n>\dfrac{40}{7}\\ \\n>5\dfrac{5}{7}$$So, at least 6 students must be enrolled in the class for the instructor to make a profit.2. If the instructor needs to make 1,000.00 profit per month, then$$f(x)\ge 1,000\\ \\70n-400\ge 1,000\\ \\7n-40\ge 100\\ \\7n\ge 140\\ \\n\ge \dfrac{140}{7}\\ \\n\ge 20$$So, at least 20 students must be enrolled in the class for the instructor to make$1,000 (or more) profit per month.