Answer:
The cost of printing posters 2 to 100 is $9.
Step-by-step explanation:
The marginal cost of printing a poster when x posters have been printed is
[tex]\dfrac{dc}{dx}=\dfrac{1}{2\sqrt{x}}[/tex]
We need to find the cost function.
Seprate the variables.
[tex]dc=\dfrac{1}{2\sqrt{x}}dx[/tex]
Integrate both sides.
[tex]\int dc=\int \dfrac{1}{2\sqrt{x}}dx[/tex]
[tex]c=\sqrt{x}+C[/tex]
where, C is an arbitrary constant.
We need to find the value of c(100)-c(1).
Substitute x=100 in the above function.
[tex]c(100)=\sqrt{100}+C=10+C[/tex]
Substitute x=1 in the above function.
[tex]c(1)=\sqrt{1}+C=1+C[/tex]
[tex]c(100)-c(1)=10+C-(1+C)[/tex]
[tex]c(100)-c(1)=10+C-1-C[/tex]
[tex]c(100)-c(1)=9[/tex]
Therefore, the cost of printing posters 2 to 100 is $9.
