To determine Luisa's profit function \( p(x) \), let's break down the problem into steps and identify the given functions for revenue \( r(x) \) and cost \( c(x) \).
Firstly, we have:
[tex]\[ r(x) = 20x \][/tex]
This tells us that the revenue for mowing \( x \) lawns is \( 20 \) times the number of lawns.
Next, we have the cost function:
[tex]\[ c(x) = 4x + 25 \][/tex]
This indicates that Luisa's cost consists of \( 4 \) times the number of lawns plus a fixed cost of \( 25 \) for gas and mower rental.
The profit function \( p(x) \) is determined by subtracting the total cost from the total revenue:
[tex]\[ p(x) = r(x) - c(x) \][/tex]
Substituting the given functions for revenue and cost:
[tex]\[ p(x) = 20x - (4x + 25) \][/tex]
We simplify this expression by distributing the negative sign and combining like terms:
[tex]\[ p(x) = 20x - 4x - 25 \][/tex]
[tex]\[ p(x) = 16x - 25 \][/tex]
So, the correct profit function \( p(x) \) is:
[tex]\[ \boxed{16x - 25} \][/tex]
Thus, the correct answer is:
D. [tex]\( p(x)=16x-25 \)[/tex]
