Question

Which kind of function best models the data in the table? Use differences or ratios.

x | y
-1 | 0.43478
0 | 1
1 | 2.3
2 | 5.29
3 | 12. 167
4 | 27.984

A). linear
B). quadratic
C). exponential
D). none of the above

Answer 1

You can use some graph tools to draw three regressions for given data. On the attached diagram you can see:

• linear function - black line;
• quadratic function - red curve;
• exponential function - blue curve.

Since

$\dfrac{2.3}{1}=2.3,\\ \\\dfrac{5.29}{2.3}=2.3,\\ \\\dfrac{12.167}{5.29}=2.3,\\ \\\dfrac{27.984}{12.167}=2.3,$

you can conclude that for the given data the best fit is exponential function with rule

$y=2.3^x.$

Answer: correct choice is C.