Question

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

Answer 1

3 - A

4 - C

Explanation:

Ques 3: From the table, we see that,

The slope of the points are given by,

`(-0.5+1)/(1-0)=0.5`

`(0+0.5)/(2-1)=0.5`

`(0.5-0)/(3-2)=0.5`

`(1-0.5)/(4-3)=0.5`

Thus, the equation of the function is,
`y=0.5x-1`.

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,

`(6.8)/(1.7)=4`

`(27.2)/(6.8)=4`

`(108.8)/(27.2)=4`

`(435.2)/(108.8)=4`

Thus, the equation of the function is,
`y=4^x`

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

So, option C is correct.