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 quadratic function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = 0, y1 = -2;
x2 = 1, y2 = 1;
x3 = 2, y3 = 10;
x4 = 3, y4 = 25;
x5 = 4, y5 = 46
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 = 1 - (-2) = 1 + 2 = 3
dy2 = y3 - y2 = 10 - 1 = 9
dy3 = y4 - y3 = 25 - 10 = 15
dy4 = y5 - y4 = 46 - 25 = 21
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 = 9 - 3 = 6
dy3 - dy2 = 15 - 9 = 6
dy4 - dy3 = 21 - 15 = 6
We observe that the difference of differences of 2 consecutive y values are constant i.e. 6.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic function.
x2 = 1, y2 = 1;
x3 = 2, y3 = 10;
x4 = 3, y4 = 25;
x5 = 4, y5 = 46
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 = 1 - (-2) = 1 + 2 = 3
dy2 = y3 - y2 = 10 - 1 = 9
dy3 = y4 - y3 = 25 - 10 = 15
dy4 = y5 - y4 = 46 - 25 = 21
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 = 9 - 3 = 6
dy3 - dy2 = 15 - 9 = 6
dy4 - dy3 = 21 - 15 = 6
We observe that the difference of differences of 2 consecutive y values are constant i.e. 6.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic function.