Question

review passage
the average weekly salary for workers in private industry nationwide is modeled by the equation ( w(t) = -0.1049t^4 + 4.3205t^3 - 64.517t^2 + 431.93t - 243.96 ), where ( t ) is the year and ( t = 0 ) denotes the year 2000.

question
in what month was the salary equal to $900? use function notation to denote this answer.

Explanation:

Step1: Set up the equation

Set $w(t) = 900$:
$$-0.1049t^4 + 4.3205t^3 - 64.517t^2 + 431.93t - 243.96 = 900$$

Step2: Rearrange the equation

Subtract 900 from both sides:
$$-0.1049t^4 + 4.3205t^3 - 64.517t^2 + 431.93t - 1143.96 = 0$$

Step3: Solve for positive t

Use a numerical method (e.g., rational root theorem, graphing calculator) to find the positive real root:
$t \approx 12.25$

Step4: Convert decimal to month

Multiply the decimal part by 12:
$0.25 \times 12 = 3$

Step5: Write in function notation

Express the result with the function:
$w(12.25) = 900$

Answer:

$w(12.25) = 900$, corresponding to March 2012