FREE SAT Interpreting Nonlinear Functions Questions and Answers 2

Question 1

The function h(t) = -4.9t^2 + bt + c models the height, in meters, of a projectile t seconds after it is launched.
The projectile reaches its maximum height of 25 meters at t = 2.
Which of the following defines the function?

Accepted Answer

h(t) = -4.9(t - 2)^2 + 25

Answer

h(t) = -4.9(t + 2)^2 + 25

Answer

h(t) = 4.9(t - 2)^2 + 25

Answer

h(t) = -4.9(t - 25)^2 + 2

Question 2

A scientist models the decay of a radioactive substance with the function A(t) = A₀(1/2)^(t/h), where A(t) is the amount remaining at time t, A₀ is the initial amount, and h is the half-life. If the half-life of the substance is 200 years, and the initial amount is 500 grams, how much of the substance remains after 800 years?

Accepted Answer

31.25 grams

Answer

125 grams

Answer

62.5 grams

Answer

15.625 grams

Question 3

The graph of y = f(x) is a parabola that opens upward with a vertex at (3, -5). The graph of y = g(x) is a line with a positive slope. If the system of equations y = f(x) and y = g(x) has exactly one solution, what must be true about the line g(x)?

Accepted Answer

The line is tangent to the parabola at its vertex.

Answer

The line is tangent to the parabola at a point where x < 3.

Answer

The line must pass through the origin.

Answer

The line is perpendicular to the parabola's axis of symmetry.

Question 4

The value of a car, V, in dollars, is modeled by the function V(t) = 25000(0.88)^t, where t is the number of years since its purchase. Which of the following statements best interprets the number 0.88 in this context?

Accepted Answer

The car retains 88% of its value from the previous year.

Answer

The car's value increases by 88% each year.

Answer

The car's value decreases by 88% each year.

Answer

The car's value decreases by $0.88 each year.

Question 5

A function is defined by f(x) = a(x-3)(x+1), where 'a' is a positive constant. A second function is g(x) = f(x) + k. For what value of k will the graph of g(x) have its vertex on the x-axis?

Accepted Answer

k = 4a

Answer

k = 2a

Answer

k = -4a

Answer

k = -a

Question 6

The number of users of a new app is modeled by the function N(d) = 100(b)^d, where d is the number of days after launch. If the number of users triples every 5 days, which of the following is the closest value for b?

Accepted Answer

1.25

Answer

3

Answer

1.5

Answer

1.20