Answer:
For the profit of $5,000, the key chains made is n = 4,000.
Step-by-step explanation:
Here the given expression , where: n = Number of key rings in thousands is given as:
P(n) = n²- 2 n - 3
Now, Profit is given to be $5,000.
Also, as we know 5000 = 5 x (1,000)
⇒ n²- 2 n - 3 = 5
Now, solving the above expression for the value of n, we get:
![n^2 - 2 n - 3 = 5\\\implies n^2 -2n - 8 = 0\\\implies n^2 -4n + 2n - 8 = 0\\\implies n(n-4) + 2(n-4) = 0\\\implies (n-4) (n+2) = 0](https://tex.z-dn.net/?f=n%5E2%20-%20%202%20n%20-%203%20%3D%205%5C%5C%5Cimplies%20%20n%5E2%20%20-2n%20-%208%20%20%3D%20%200%5C%5C%5Cimplies%20%20n%5E2%20%20-4n%20%2B%20%202n%20-%208%20%20%3D%20%200%5C%5C%5Cimplies%20n%28n-4%29%20%20%2B%202%28n-4%29%20%20%3D%200%5C%5C%5Cimplies%20%28n-4%29%20%28n%2B2%29%20%20%3D%200)
So, n = 4, OR , n = -2
Now, as n = The number of key chains. So it CANNOT BE NEGATIVE.
So, n= 4 = 4 x (1,000) = 4,000 key rings.
Hence, for the profit of $5,000, the key chains made is n = 4,000.