Question

The projected sales volume of a video game cartridge is given by the function s(p)= 3000/(2p+a), where s is the number of cartridges sold, in thousands; p is the price per cartridge in dollars; and a is a constant. If according to the projections, 100,000 cartridges are sold at $10 per cartridge, how many cartridges will be sold at $20 per cartridge?

Answer 1

@pgpilot326

Answer 2

Use the initial info to determine the values of a and then you can change the price to see what the new sales volume will be.

Answer 3

"value of a"

Answer 4

I tried that, but I still have difficulty

Answer 5

I don't understand how the give correlates with the one I am trying to find @pgpilot326

Answer 6

\[s \left( p \right)=\frac{ 3000 }{ 2p+a }\]
We know s(10) so from this we can determine the value of a. Once you have this then s(p) will only have p as a variable. Then you can plug in 20 for p and see what s(20) is.

Answer 7

@pgpilot326 So do I multiply 2(10)+a with 100,000

Answer 8

yeah...\[s(10) = 100,000 = \frac{ 3000 }{ 2(10) +a }\]

and solve for a. then plug in 20 for p and you'll have s(20)

Answer 9

I get -1997000 for a. But that doesn't seem very reasonable @pgpilot326

Answer 10

let me check

Answer 11

\[a=\frac{ 3000 }{ 100000 }-20=.03 - 20 = -19.97\]

Answer 12

@pgpilot326 So do I just plug that in?

Answer 13

now you have \[s(p)=\frac{ 3000 }{ 2p-19.97 }\]just plug in 20 for p and evaluate.

Answer 14

@pgpilot326 Thanks!