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

Question

x y

0, 1.3

1, 7.8

2, 46.8

3, 280.8

4, 1684.8

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

Answer 1

nope. Check and you will see that each value is multiplied by 6 to get the next in the list.

quadratic relations have a constant 2nd difference.

Answer 2

7.8 / 1.3 = 6

46.8 / 7.8 = 6

280.8 / 46.8 = 6

1684.8 / 280.8 = 6

Your data for y is a geometric sequence
( a sequence of numbers in which the ratio between consecutive terms is constant).

The n-th term of a geometric sequence with initial value a1 and common ratio r is given by:

an = a1 ∙ r ⁿ⁻¹

In this case a1 = 1.3 , r = 6

an = 1.3 ∙ 6 ⁿ⁻¹

This mean your function is:

y = 1.3 ∙ 6 ˣ⁻¹

1.3 ∙ 6 ˣ⁻¹ is exponential function

Answer C

Answer 3

thx Bosnian

Answer 4

0 1.7
1 6.8
2 27.2
3 108.2
4 435.2

What kind of equation is this?

Answer 5

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

x y
0 1.3
1 7.8
2 46.8
3 280.8
4 1684.8

Answer 6

The ratio between consecutive terms of y is constant, which indicates an exponential function best models the data.

So, an exponential function equation with the form y = ab^x where a and b are constants is:

y = 1.3 * 6^x

Therefore, the answer is C) exponential.