Question

In complete two or more sentences, determine the appropriate model for the given data and explain how you made your decision. (1,0), (2,1.5), (5,2.5), (8,3)

Answer 1

Answer:

The model for the given point is $y=1.4004\ln (x) + 0.2158$                                              

Step-by-step explanation:

Given : Data  (1,0), (2,1.5), (5,2.5), (8,3).

To find : Determine the appropriate model for the given data?

Solution :

Data  (1,0), (2,1.5), (5,2.5), (8,3).

We plot the data points on the graph and get the best fit line using trend line of the function.

Using regression calculator,

The function has a logarithmic behavior so the best line which represent the data is given by

$y=1.4004\ln (x) + 0.2158$

and the value of R² i.e. correlation coefficient is given by

$R^2=0.9691$ which is approximately equal to 1 gives you the best fit line.

Therefore, The model for the given point is $y=1.4004\ln (x) + 0.2158$

Refer the attached figure below.

Answer 2

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