Question

a kids pool had a small opening through which water sometimes leaked out. water was poured into the pool from time to time. the graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours. which of the following statements best describes the amount of water in the pool? a it is increasing during the time interval 4 < x < 7 hours. b it is increasing during the time interval 10 < x < 50 hours. c it is decreasing during the time interval 4 < x < 7 hours. d it is decreasing during the time interval 10 < x < 50 hours. question 7 (4 points) (02:03 hc) the following table shows the number of feet a bird flies above the ground as a function of time: time (in seconds) x distance above ground (in feet) f(x) 0 21 2 18 4 15 6 12 8 9 find and interpret the meaning of the x - intercept in this scenario. a (21,0); the time it takes for the bird to reach the ground b (14,0); the time it takes the bird to reach its highest point c (21,0); the time it takes the bird to reach its highest point d (14,0); the time it takes for the bird to reach the ground

Explanation:

Step1: Analyze the pool - water graph

For the graph of water in the pool, the x - axis represents time (in hours) and the y - axis represents the amount of water (in gallons). A function is increasing when the y - values increase as the x - values increase. Looking at the graph, we can see that the amount of water is increasing in the interval \(4 < x<7\) hours.

Step2: Analyze the bird - flight table

For the bird - flight table, the x - values represent time (in seconds) and the f(x) values represent the distance above the ground (in feet). The x - intercept is the value of x when f(x)=0. We first find the linear relationship between x and f(x). The slope \(m=\frac{\Delta y}{\Delta x}=\frac{18 - 21}{2-0}=-\frac{3}{2}\). Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((0,21)\), we have \(y-21=-\frac{3}{2}x\), or \(y = 21-\frac{3}{2}x\). Setting \(y = 0\), we get \(0=21-\frac{3}{2}x\), then \(\frac{3}{2}x=21\), and \(x = 14\). The x - intercept \((14,0)\) represents the time it takes for the bird to reach the ground.

Answer:

a. It is increasing during the time interval \(4 < x<7\) hours.
d. \((14,0)\); the time it takes for the bird to reach the ground.