Question

which type of model is most appropriate for the following data?

$x$	$y$
2	3.45
3	4.9
4	7.96
5	12.65
6	20.78
7	32.6
8	52.6

Explanation:

Step1: Calculate first - differences

$3.45 - 1.71=1.74$, $4.9 - 3.45 = 1.45$, $7.96 - 4.9=3.06$, $12.65 - 7.96 = 4.69$, $20.78 - 12.65 = 8.13$, $32.6 - 20.78 = 11.82$, $52.6 - 32.6 = 20$. First - differences are not constant.

Step2: Calculate second - differences

$1.45-1.74=- 0.29$, $3.06 - 1.45 = 1.61$, $4.69 - 3.06 = 1.63$, $8.13 - 4.69 = 3.44$, $11.82 - 8.13 = 3.69$, $20 - 11.82 = 8.18$. Second - differences are not constant.

Step3: Calculate ratios

$\frac{3.45}{1.71}\approx2.02$, $\frac{4.9}{3.45}\approx1.42$, $\frac{7.96}{4.9}\approx1.62$, $\frac{12.65}{7.96}\approx1.59$, $\frac{20.78}{12.65}\approx1.64$, $\frac{32.6}{20.78}\approx1.57$, $\frac{52.6}{32.6}\approx1.61$. The ratios of consecutive $y$ - values are approximately constant. So, an exponential model is most appropriate.

Answer:

Exponential model