Answer: 149 cartridges will be sold at 20 dollars per cartridge.
Step-by-step explanation:
Given: The projected sales volume of a video game cartridge is given by the function [tex]s(p)=\dfrac{3000}{2p+a}[/tex], where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant.
Put s(p)=100000, p= 10, we get
[tex]100000=\dfrac{3000}{2(10)+a}\\\\\Rightarrow\ 100=\dfrac{3}{20+a}\\\\\Rightarrow\ 100(20+a)=3\\\\\Rightarrow\ 2000+100a=3\\\\\Rightarrow\ 100a=-1997\\\\\Rightarrow\ a=-19.97[/tex]
i.e. [tex]s(p)=\dfrac{3000}{2p-19.97}[/tex]
Put p=20, we get
[tex]s(20)=\dfrac{3000}{2(20)-19.97}\\\\=\dfrac{3000}{40-19.97}\\\\=\dfrac{3000}{20.03}\approx149[/tex]
Hence, 149 cartridges will be sold at 20 dollars per cartridge.
