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: The given function is a quadratic function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = 0, y1 = 1;
x2 = 1, y2 = 2;
x3 = 2, y3 = 7;
x4 = 3, y4 = 16;
x5 = 4, y5 = 29
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 = 2 - 1 = 1
dy2 = y3 - y2 = 7 - 2 = 5
dy3 = y4 - y3 = 16 - 7 = 9
dy4 = y5 - y4 = 29 - 16 = 13
We observe that the difference for every consecutive x values is constant i.e. 1 but for y values the difference are not constant.
Hence, the given function is not a linear function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 5 - 1 = 4
dy3 - dy2 = 9 - 5 = 4
dy4 - dy3 = 13 - 9 = 4
We observe that the difference of differences of 2 consecutive y values are constant i.e. 4.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic function.
x2 = 1, y2 = 2;
x3 = 2, y3 = 7;
x4 = 3, y4 = 16;
x5 = 4, y5 = 29
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 = 2 - 1 = 1
dy2 = y3 - y2 = 7 - 2 = 5
dy3 = y4 - y3 = 16 - 7 = 9
dy4 = y5 - y4 = 29 - 16 = 13
We observe that the difference for every consecutive x values is constant i.e. 1 but for y values the difference are not constant.
Hence, the given function is not a linear function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 5 - 1 = 4
dy3 - dy2 = 9 - 5 = 4
dy4 - dy3 = 13 - 9 = 4
We observe that the difference of differences of 2 consecutive y values are constant i.e. 4.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic 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
