Question
Determine whether the data are best modelled by a linear , quadratic or exponential function ?
![](data:image/png;base64,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)
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.
is constant for any value of n, the function is known as an exponential function.
The correct answer is: The given function is a linear function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = -2, y1 = 2;
x2 = -1, y2 = 7;
x3 = 0, y3 = 12;
x4 = 1, y4 = 17;
x5 = 2, y5 = 22
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = -1 - (-2) = -1 + 2 = 1
dx2 = x3 - x2 = 0 - (-1) = 0 + 1 = 1
dx3 = x4 - x3 = 1 - 0 = 1
dx4 = x5 - x4 = 2 - 1 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = 7 - 2 = 5
dy2 = y3 - y2 = 12 - 7 = 5
dy3 = y4 - y3 = 17 - 12 = 5
dy4 = y5 - y4 = 22 - 17 = 5
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. 5.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.
x2 = -1, y2 = 7;
x3 = 0, y3 = 12;
x4 = 1, y4 = 17;
x5 = 2, y5 = 22
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = -1 - (-2) = -1 + 2 = 1
dx2 = x3 - x2 = 0 - (-1) = 0 + 1 = 1
dx3 = x4 - x3 = 1 - 0 = 1
dx4 = x5 - x4 = 2 - 1 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = 7 - 2 = 5
dy2 = y3 - y2 = 12 - 7 = 5
dy3 = y4 - y3 = 17 - 12 = 5
dy4 = y5 - y4 = 22 - 17 = 5
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. 5.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.