A reality TV show has a model where they vote off a number of contestants each week. The graph shows how many contestants they start the season with, and how many they vote off each episode. What is the rate of change?

Question

(1 point)
The rate of change is
Question 9
9.

The NCAA Basketball Championship (also known as March Madness) is an example of exponential decay. At each round of the tournament, teams play against one another with only the winning teams progressing to the next round. In other words, the number of teams playing at each round is half of the number of teams playing in the previous round. The equation f(x)= 64(0.50)x
represents the pattern in this situation. Define an appropriate range for this situation.

(1 point)
Responses

1 ≤ x ≤ 64
1 ≤ x ≤ 64

1 ≤ y ≤ 64
1 ≤ y ≤ 64

64 ≤ y ≤ 1
64 ≤ y ≤ 1

64 ≤ x ≤ 1
64 ≤ x ≤ 1
Question 10
10.

A ball is launched upward at 48 feet per second from a platform that is 100 feet high. The function that models this situation is h(t)=−16t2+48t +100
where t is the time in seconds and h(t) is the height of the ball.

Find the maximum height the ball reaches and how long it will take to get there.

What key feature of the graph is the problem asking you to find?



(1 point)
Responses

the x intercept
the x intercept

the vertex
the vertex

The y-intercept
The y-intercept

the rate of change
the rate of change

the axis of symmetry
the axis of symmetry
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Answer 1

Question 9:

For the NCAA Basketball Championship, the equation \( f(x) = 64(0.50)^x \) describes the number of teams remaining after each round \( x \). Since the tournament starts with 64 teams and halves the number of teams after each round, the appropriate range for \( x \) (the number of rounds) can be defined as:

Answer: \( 0 \leq x \leq 6 \)

(The total number of rounds is from 0 to 6, since the last round begins with 2 teams and concludes with 1 winner.)

Question 10:

The function that models the height of the ball over time is \( h(t) = -16t^2 + 48t + 100 \), which is a quadratic function. The maximum height of the ball corresponds to the vertex of this parabola.

Answer: the vertex

For the problem, finding the maximum height and the time it takes to reach that height involves determining the vertex of the quadratic function.