Polynomial Technology Worksheets Grade 12

1. A biomedical engineer is modeling the concentration of a new drug in a patient's bloodstream using the polynomial function C(t) = -0.02t³ + 0.3t² + 0.5t, where t represents hours after administration and C(t) is measured in milligrams per liter. The drug is considered effective when the concentration is increasing and safe when the concentration is decreasing. Determine the time interval during which the drug is both effective and safe according to this model.
2. Use Desmos to graph f(x)=x³-9x²+23x-15 and find the sum of all x-coordinates where the local maximum and minimum occur.
3. A biomedical engineer is modeling the concentration of a new drug in a patient's bloodstream using the polynomial function C(t) = -0.02t³ + 0.3t² + 0.5t, where C is the concentration in milligrams per liter and t is time in hours after administration. The drug is considered effective when the concentration is increasing and above 1 mg/L. Determine the time interval during which the drug remains effective.

…and 3 more problems

1. A biomedical engineer is modeling the concentration of a new medication in a patient's bloodstream over time. The concentration C(t) in milligrams per liter is given by the polynomial function C(t) = -0.02t³ + 0.45t² - 2.7t + 5 for 0 ≤ t ≤ 15 hours. At what time does the medication reach its maximum concentration in the bloodstream, and what is that maximum concentration?
2. A polynomial function f(x) is graphed on a coordinate plane. The graph shows three x-intercepts at (-2, 0), (1, 0), and (3, 0). The graph passes through the point (0, -6) and has end behavior where f(x) → -∞ as x → -∞ and f(x) → +∞ as x → +∞. Determine the equation of the polynomial function in factored form.
3. Use Desmos to graph f(x) = x^4 - 18x^3 + 109x^2 - 252x + 180 and find the sum of all distinct real zeros.

…and 5 more problems

1. Liam is designing a roller coaster and needs to analyze the polynomial function f(x) = x³ - 6x² + 9x + 2 that models the track's elevation. He wants to determine the intervals where the track is increasing in elevation. Find all x-values where f'(x) > 0.
2. Use Desmos to graph f(x)=x³-9x²+24x-16 and find the sum of all x-coordinates where the local maximum and minimum occur.
3. Use Desmos to graph f(x)=x⁴-8x³+22x²-24x+8 and find the sum of all x-coordinates where the graph has local minima.

…and 4 more problems