Water towers are tall to provide enough water pressure to supply all of the houses and
businesses in the area of the tower. Each foot of height provides 0.43 psi (pounds per
square inch) of pressure.
a. Write a sequence for the pressure in psi for each foot of height.
0.43,0.86,1.29,1.72,2.15...=51.6 (up to 15th term)
b. What is the minimum height that supplies 50 psi, a typical minimum supply pressure?
116.3 ft
c. What is the minimum height that supplies 100 psi, which is a typical maximum pressure?
232.5 ft
d. Graph the sequence, and discuss the relationship between the height found for a pressure of 50 psi and the height found at 100 psi.
I know answers to a,b,c but Im having trouble with part d
if you know a,b,c then you can easily write the linear function
p(h)
Then just
solve for h when p=50 or p=100
since it's a linear function you should find that the 2nd height is twice as high as the first
In order to graph the sequence and understand the relationship between the height for a pressure of 50 psi and the height for a pressure of 100 psi, we can plot the height on the x-axis and the pressure on the y-axis.
For this particular sequence, we know that each foot of height provides 0.43 psi of pressure. So, we can start by plotting the points for the given sequence:
(1, 0.43), (2, 0.86), (3, 1.29), (4, 1.72), ...
To find the point on the graph for a pressure of 50 psi, we can use the formula:
height = pressure / 0.43
Substituting the given pressure of 50 psi:
height = 50 / 0.43
Calculating this, we find that the height is approximately 116.3 ft.
Similarly, to find the point on the graph for a pressure of 100 psi, we use the same formula:
height = pressure / 0.43
Substituting the given pressure of 100 psi:
height = 100 / 0.43
Calculating this, we find that the height is approximately 232.5 ft.
Now, we plot these two points on the graph: (116.3, 50) and (232.5, 100).
By connecting these two points with a line, we can see that the relationship between the height and pressure is linear. As the height increases, the pressure also increases according to the slope of the line, which is 0.43 psi per foot.
In other words, for every foot of height increase, the pressure increases by 0.43 psi. This linear relationship holds true for all heights and pressures within the given context.
Therefore, by graphing the sequence and analyzing the relationship between the height and pressure, we can better understand how the water towers provide the necessary pressure to supply houses and businesses in the area.