2. Advanced Algebra

Polynomial Modeling — Quiz

Test your understanding of polynomial modeling with 5 practice questions.

Practice Questions

Question 1

A polynomial function $P(x)$ models the population of a city over $x$ years. If the end behavior of the polynomial shows $P(x) \to \infty$ as $x \to \infty$, and $P(x) \to \infty$ as $x \to -\infty$, which of the following statements about the degree and leading coefficient of $P(x)$ must be true?

Question 2

The height of a projectile, $h(t)$, in meters, is modeled by the polynomial function $h(t) = -4.9t^2 + 20t + 5$, where $t$ is the time in seconds. What is the initial velocity of the projectile?

Question 3

A company's monthly revenue, $R(x)$, in thousands of dollars, from selling $x$ units of a product is modeled by the polynomial function $R(x) = -0.01x^3 + 0.5x^2 + 20x$. To find the number of units that maximizes revenue, which of the following steps is most appropriate?

Question 4

The value of a car, $V(t)$, in thousands of dollars, $t$ years after purchase is modeled by the polynomial function $V(t) = 0.05t^3 - 0.8t^2 - 5t + 30$. What is the predicted value of the car after $2$ years?

Question 5

The population of a certain type of bacteria, $P(t)$, in millions, after $t$ hours is modeled by the polynomial function $P(t) = -0.02t^4 + 0.5t^3 - 4t^2 + 10t + 50$. What does the leading coefficient ($-0.02$) indicate about the long-term population trend?