Answer:
A) Independent variable is "c"
Dependent variable is "p"
B) Yes, it's a function
C) p = 7c - 31
D)domain of the function: 0 ≤ c ≤ 40
Range of the function: 0 ≤ p ≤ 249
Step-by-step explanation:
A) c is the total number of cars washed and p is the profit. The profit depends on the total number of cars washed. Hence, profit(p) is the dependent variable while "c" is independent variable
B) Yes it's a function because for each number of cars washed, there is a distinct value of profit made.
C) We are told that the liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$.
$31 is cost to wash one car. Thus profit made per car is;
p = 7c - 31
D) The cost of $31 liquid soap is enough to only wash a maximum of 40 cars. This means the domain for the cars is from 0 cars to 40 cars
Thus;
domain of the function is 0 ≤ c ≤ 40
The profit function is given in answer C above as p = 7c - 31.
Now, if 0 cars are washed they will make zero profit but if 40 cars are washed then;
p = 7(40) - 31
p = 280 - 31
p = 249
Range of the function: 0 ≤ p ≤ 249
