FREE SAT Interpreting Nonlinear Functions Questions and Answers

Question 1

The height `h`, in meters, of a ball thrown upwards from a building is modeled by the function `h(t) = -4.9t^2 + 20t + 40`, where `t` is the time in seconds after the ball is thrown.
Based on the model, what is the meaning of the number 40 in this context?

Accepted Answer

The initial height from which the ball was thrown.

Answer

The maximum height the ball reaches.

Answer

The time it takes for the ball to hit the ground.

Answer

The initial speed of the ball.

Question 2

The number of bacteria in a colony is modeled by the function `P(t) = 500(1.08)^t`, where `t` is the time in hours. Which of the following best describes the meaning of the number 1.08 in the function?

Accepted Answer

The number of bacteria increases by 8% each hour.

Answer

The initial number of bacteria was 108.

Answer

The number of bacteria increases by 1.08 each hour.

Answer

The number of bacteria reaches its maximum in 1.08 hours.

Question 3

The profit, `P`, in thousands of dollars, from selling a product at a price of `x` dollars per unit is given by the function `P(x) = -2x^2 + 80x - 600`. The graph of this function is a parabola that opens downward. What does the vertex of the parabola represent?

Accepted Answer

The price that results in the maximum profit.

Answer

The price at which the profit is zero.

Answer

The initial cost of producing the product.

Answer

The number of units sold.

Question 4

The value of a car, `V`, in dollars, `t` years after its purchase is modeled by the function `V(t) = 25000(0.85)^t`. A graph of this function is created. What does the y-intercept of the graph represent in this context?

Accepted Answer

The initial purchase price of the car.

Answer

The value of the car after one year.

Answer

The annual rate of depreciation of the car.

Answer

The number of years it takes for the car's value to be zero.

Question 5

The amount of a certain medication, `A`, in milligrams, in a patient's bloodstream `t` hours after administration is given by `A(t) = 100(0.5)^(t/4)`. What does the number 4 represent in this function?

Accepted Answer

The half-life of the medication in hours.

Answer

The initial dose of the medication in milligrams.

Answer

The number of hours it takes for the medication to be completely eliminated.

Answer

The percentage of medication that decays each hour.

Question 6

The height of a rocket, `h`, in feet, `t` seconds after launch is modeled by `h(t) = -16t^2 + 224t`. At what time `t` does the rocket reach its maximum height?

Accepted Answer

7 seconds

Answer

4 seconds

Answer

14 seconds

Answer

224 seconds

Question 7

A researcher models the spread of a rumor in a school of 1000 students using the function `N(t) = 1000 / (1 + 999e^(-0.5t))`, where `N(t)` is the number of students who have heard the rumor after `t` days. According to the model, what is the best interpretation of the number 1000?

Accepted Answer

The maximum number of students who can hear the rumor.

Answer

The initial number of students who started the rumor.

Answer

The number of days it takes for the rumor to spread to half the students.

Answer

The rate at which the rumor is spreading.

The height `h`, in meters, of a ball thrown upwards from a building is modeled by the function `h(t) = -4.9t^2 + 20t + 40`, where `t` is the time in seconds after the ball is thrown.Based on the model, what is the meaning of the number 40 in this context?

The height `h`, in meters, of a ball thrown upwards from a building is modeled by the function `h(t) = -4.9t^2 + 20t + 40`, where `t` is the time in seconds after the ball is thrown.
Based on the model, what is the meaning of the number 40 in this context?