We are tasked with substituting $x = 2000$ into the quadratic equation:

$y' = -0.03807692415x^2 + 152.74523902x - 153180.8703.$

Step 1: Substitution of $x = 2000$

We substitute $x = 2000$ into the equation:

$y' = -0.03807692415(2000)^2 + 152.74523902(2000) - 153180.8703.$

Step 2: Calculating Each Term

1. Compute $(2000)^2$:

$2000^2 = 4000000.$

2. Multiply by $-0.03807692415$:

$-0.03807692415 \times 4000000 = -152307.6966.$

3. Multiply $152.74523902 \times 2000$:

$152.74523902 \times 2000 = 305490.47804.$

4. Combine all terms:

$y' = -152307.6966 + 305490.47804 - 153180.8703.$

Step 3: Final Calculation

Now perform the addition and subtraction step by step:

1. Add $-152307.6966$ and $305490.47804$:

$-152307.6966 + 305490.47804 = 153182.78144.$

2. Subtract $153180.8703$:

$153182.78144 - 153180.8703 = 1.91114.$

Final Answer:

$y' = 1.91114$

Let me know if you need further clarifications or detailed steps!

Related Questions:

1. How do you solve a quadratic equation for any value of $x$?
2. What are the applications of quadratic functions in real-life problems?
3. How can you determine the vertex of a quadratic equation?
4. What is the process for factoring a quadratic equation?
5. How do you find roots of a quadratic equation using the quadratic formula?

Tip:

When substituting into equations, calculate each term separately to avoid errors. This ensures clarity and accuracy in results.