Question

Determine whether the exponential model y = a ekt or the power model y = a zb is the best fit to the following data. Then find the equation of that model. 1.2 2.0 2.8 3.6 5.1 6.3 7.5 9.3 10.9 12.1 14.6 y 5.31 4.92 4.51 4.19 3.59 3.18 2.69 2.37 2.021.79 1.40

Answer 1

Solution :

We plot the given data using graphing calculator to get the best fit line of the model.

First we plot an exponential series of the data, shown in the graph below

6 un y = 5.958e-0.1% R? = 0.998 4 3 Series1 2 Expon. (Series1) 1 0 0 10 1 Մ 5 20

The exponential series model is given $y=5.958e^{-0.1x}$ .

i.e. $y=ae^{kx}\Rightarrow y=5.958e^{-0.1x}$

Here, a=5.958, k=-0.1.

Now, we plot an power series of the data, shown in the graph below

7 LD y= 7.271x-052 R = 0.906 5 4 3 Series1 Power (Series1) N 1 0 0 5 10 15 20

The power series model is given $y=7.271x^{-0.52}$ .

i.e. $y=ax^b\Rightarrow y=7.271x^{-0.52}$

Here, a=7.271, b=-0.52.

Now, we compare these two graph we seen that the best fit line curve is shown in exponential series.

Therefore, The equation of the model is exponential model  $y=5.958e^{-0.1x}$.