The function y=128−8x models the amount of water, in ounces, left in Tariq’s water jug after pouring x servings of water. Which of the following statements properly interprets a key feature of the model?

Question

Responses

Before any servings are poured, the jug contains 128 ounces of water. - correct

Before any servings are poured, the jug contains 8 ounces of water. - incorrect

Each serving increases the total water in the jug by 8 ounces. - incorrect

Each serving consists of 128 ounces of water. - incorrect

explain how you get the correct answer

Answer 1

To get the correct answer, we need to look at the equation y=128−8x.

When x=0, the equation becomes y=128-8(0) which simplifies to y=128. This means that when no servings are poured (x=0), there are 128 ounces of water in the jug.

Therefore, the correct statement is: Before any servings are poured, the jug contains 128 ounces of water.

Answer 2

A scientist is growing cells in a petri dish. Which of the following equations could model the number of cells in the petri dish after x days?
Responses

y=100(0.2)x
y is equal to 100 times 0 point 2 to the x th power - incorrect

y=(14)x
y is equal to 1 fourth to the x th power - incorrect

y=15(0.99)x
y is equal to 15 times 0 point 9 9 to the x th power - incorrect

y=10(2)x - correct

explain how you get the correct answer

Answer 3

To determine the correct equation to model the number of cells in the petri dish after x days, we can look at the structure of exponential growth.

The correct equation for exponential growth is in the form y = a(b)^x, where "a" is the initial amount, "b" is the growth factor, and x is the number of days.

In the equation y=10(2)x, we have an initial amount of 10 cells (a=10) and a growth factor of 2 (b=2). This means that the number of cells doubles every day.

Therefore, the correct equation to model the number of cells in the petri dish after x days is y=10(2)x.

Answer 4

A new high school opened in 2018 with an initial enrollment of 1,500 students. The number of students attending, S, grows as a linear function of time, t, where t is the number of years since the school’s opening. In 2022, there were 1,900 students enrolled. Sketch a graph of the situation. Where would you place the y-intercept?
Responses

(0, 1,900) - incorrect

(0, 1,500) - correct

(1,900, 0) - incorrect

(1,500, 0) - incorrect

explain how you get the correct answer

Answer 5

The initial enrollment of the high school in 2018 was 1,500 students, which means that the y-intercept of the graph should be at the point (0, 1,500). This is because the y-intercept represents the value of the function when t=0, that is, at the beginning or the starting point.

Therefore, the correct placement of the y-intercept on the graph should be at (0, 1,500).