Question
Determine whether a linear , quadratic or exponential function is the best model for the data in each table .
Hint:
1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. When the difference between 2 consecutive differences for output values (y values) for a given constant change in the input values (x values) is constant. i.e. dy(n)- dy(n-1) is constant for any value of n, the function is known as a quadratic function.
3. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. y(n)/y(n-1) is constant for any value of n, the function is known as an exponential function.
The correct answer is: Final Answer:- ∴ The given function is a linear function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = 0, y1 = -6;
x2 = 1, y2 = -3;
x3 = 2, y3 = 0;
x4 = 3, y4 = 3;
x5 = 4, y5 = 6
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 1 - 0 = 1
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = -3 - (-6) = -3 + 6 = 3
dy2 = y3 - y2 = 0 - (-3) = 0 + 3 = 3
dy3 = y4 - y3 = 3 - 0 = 3
dy4 = y5 - y4 = 6 - 3 = 3
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is constant i.e. 3.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.
x2 = 1, y2 = -3;
x3 = 2, y3 = 0;
x4 = 3, y4 = 3;
x5 = 4, y5 = 6
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 1 - 0 = 1
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = -3 - (-6) = -3 + 6 = 3
dy2 = y3 - y2 = 0 - (-3) = 0 + 3 = 3
dy3 = y4 - y3 = 3 - 0 = 3
dy4 = y5 - y4 = 6 - 3 = 3
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is constant i.e. 3.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.
Check for extraneous solutions
,where H is the height in centimeters and M is the mass in kilograms. A doctor calculates a particular dose of medicine for a patient whose BSA is less than 1.9. If the patient is 160 cm tall, what must the mass of the person be for the dose to be appropriate?
Check for extraneous solutions
