5. Functions & Modeling

Modeling Practice — Quiz

Test your understanding of modeling practice with 5 practice questions.

Practice Questions

Question 1

A company's monthly profit, $P(x)$, from selling $x$ units of a product is modeled by the function $P(x) = -0.5x^2 + 20x - 150$. What type of function is this, and what does the negative coefficient of the $x^2$ term imply about the profit?

Question 2

The population of a town, $P(t)$, in thousands, $t$ years after 2000 is modeled by the function $P(t) = 25e^{0.03t}$. What type of function is this, and what does the constant $0.03$ represent in the context of the population?

Question 3

A scientist is studying the decay of a radioactive substance. The amount of substance remaining, $A(t)$, after $t$ hours is given by $A(t) = A_0 (0.85)^t$, where $A_0$ is the initial amount. What type of function is this, and what does the base $0.85$ signify?

Question 4

The height, $h(t)$, in meters, of a projectile launched upwards is given by the function $h(t) = -4.9t^2 + 30t + 5$, where $t$ is the time in seconds. What type of function is this, and how can you find the maximum height of the projectile?

Question 5

A company's revenue, $R(x)$, from selling $x$ units of a product is modeled by $R(x) = 100x - 0.1x^2$. To maximize revenue, the company needs to find the number of units $x$ that corresponds to the maximum point of this function. What mathematical concept is used to find this maximum?