The amount of pressure on a diver as she descends into the sea can be modeled by the equation y=1\10x+1
, where x is her depth in meters and y is the amount of pressure in atmospheres (atm). Which of these statements are correct according to the model? Select TWO that apply.
A.
For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
B.
For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
C.
For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
D.
For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
E.
At sea level, the amount of pressure on the diver is
atm.
F.
At sea level, the amount of pressure on the diver is 1 atm.
The correct statements according to the model are:
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
F. At sea level, the amount of pressure on the diver is 1 atm.
The correct statements according to the model are:
B. For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atm.
D. For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
Therefore, options B and D are correct.
To determine which statements are correct according to the model, we need to analyze the given equation: y = 1/10x + 1, where x represents the depth in meters and y represents the amount of pressure in atmospheres (atm).
A. For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atm.
To evaluate this statement, we substitute x = 1 into the equation to find y(1):
y(1) = 1/10(1) + 1
y(1) = 1/10 + 1
y(1) = 1/10 + 10/10
y(1) = 11/10
Since y(1) = 11/10 is greater than 1 atm, this statement is incorrect.
B. For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atm.
To evaluate this statement, we substitute x = 1 into the equation to find y(1):
y(1) = 1/10(1) + 1
y(1) = 1/10 + 1
y(1) = 1/10 + 10/10
y(1) = 11/10
Since y(1) = 11/10 is greater than 1 atm, this statement is incorrect.
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
To evaluate this statement, we substitute x = 10 into the equation to find y(10):
y(10) = 1/10(10) + 1
y(10) = 1 + 1
y(10) = 2
Since y(10) = 2 atm, this statement is incorrect.
D. For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
To evaluate this statement, we substitute x = 10 into the equation to find y(10):
y(10) = 1/10(10) + 1
y(10) = 1 + 1
y(10) = 2
Since y(10) = 2 atm, this statement is incorrect.
E. At sea level, the amount of pressure on the diver is 1 atm.
To evaluate this statement, we substitute x = 0 (sea level) into the equation to find y(0):
y(0) = 1/10(0) + 1
y(0) = 0 + 1
y(0) = 1
Since y(0) = 1 atm, this statement is correct.
F. At sea level, the amount of pressure on the diver is 1 atm.
This statement is the same as statement E and thus is also correct.
Therefore, the correct statements are E and F.