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For questions 3-4 which kind of function best models the data in the table? use differences or ratios.


x y
_____
0 -1
1 -0.5
2 0
3 0.5
4 1

a)liner
b)quadratic
c)exponential
d)none of these



x y
_____
o 1.7
1 6.8
2 27.2
3 108.8
4 435.2

a)liner
b)quadratic
c)exponential
d)none of these

Respuesta :

Answer:

3 - A

4 - C

Step-by-step explanation:

Ques 3: From the table, we see that,

The slope of the points are given by,

[tex]\frac{-0.5+1}{1-0}=0.5[/tex]

[tex]\frac{0+0.5}{2-1}=0.5[/tex]

[tex]\frac{0.5-0}{3-2}=0.5[/tex]

[tex]\frac{1-0.5}{4-3}=0.5[/tex]

Thus, the equation of the function is, [tex]y=0.5x-1[/tex].

So, the best function for this model is a linear function.

Hence, option A is correct.

Ques 4: From the table, we have,

The change in the y-values is,

[tex]\frac{6.8}{1.7}=4[/tex]

[tex]\frac{27.2}{6.8}=4[/tex]

[tex]\frac{108.8}{27.2}=4[/tex]

[tex]\frac{435.2}{108.8}=4[/tex]

Thus, the equation of the function is, [tex]y=4^x[/tex]

Hence, the best function for the model is an exponential function.

So, option C is correct.

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