Question

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

y X
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

a. linear
b. quadratic
c. exponential
d. none of the above

Answer 1

THE ANSWER IS LETTER C

Answer 2

Option C exponential.

Explanation:

To find the function best models the data in the table we will find the common ratio first. If the common ratios of the function are same then it's an exponential function.

For x = 0 and x = 1

`(f(1))/(f(0))=(6.8)/(1.7)=4`

For x = 1 and x = 2

`(f(2))/(f(1))=(27.2)/(6.8)=4`

For x = 2 and x = 3

`(f(3))/(f(2))=(108.8)/(27.2)=4`

Now we are sure that it's an exponential function.

For linear function common difference should be same in each term.

f(1) - f(0) = 6.8 - 1.7 = 5.1

f(2) - f(1) = 27.2 - 6.8 = 20.4

Therefore it's neither a linear function nor quadratic function.

Option C. is the correct option.