ACT (Enhanced)MathematicsMedium
A machine operator is setting up a new production line. The total cost, C(x), in dollars, to produce x units of a product is given by the function C(x) = 0.5x² + 20x + 500. If the machine produces 100 units, what is the total cost?
- A$2550
- B$4500
- C$7550
- D$7500
Show answer & explanationAnswer & explanation
Correct answer: C. $7550
To find the total cost for 100 units, substitute x = 100 into the cost function: C(100) = 0.5(100)² + 20(100) + 500. This simplifies to C(100) = 0.5(10000) + 2000 + 500 = 5000 + 2000 + 500 = 7500 + 500 = 7550 dollars.
Why the other options are wrong
- A. This might result from a calculation error, perhaps omitting the 0.5 multiplier or squaring incorrectly.
- B. This would result if the constant term was omitted or other calculation errors occurred.
- D. This is almost correct, but misses the final constant term of 500.
Quadratic Function Evaluation
Evaluating a quadratic function involves substituting a specific value for the independent variable (x) into the function's equation and then performing the arithmetic operations to find the corresponding output (y).
- Quadratic functions are typically of the form ax² + bx + c.
- Follow the order of operations (PEMDAS/BODMAS).
- Careful with squaring negative numbers (if applicable).
Memory trick: Plug in, square, multiply, then add it all up.