PLEASE HELP ME

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

X | Y

0 | 0.6

1 | 4.2

2 | 29.4

3 | 205.8

4 | 1440.6

A. Linear

B. Quadratic

C. Exponential

D. None or the above

C. Exponential

Step-by-step explanation:

If the function is linear, the differences will be equal.

d₁ = y₁ − y₀ = 4.2 − 0.6 = 3.6

d₂ = y₂ − y₁ = 29.4 − 4.2 = 25.2

d₃ = y₃ − y₂ = 205.8 − 29.4 = 176.4

d₄ = y₄ − y₃ = 1440.6 − 205.8 = 1234.8

The differences are not equal, so this is not linear.

If the function is quadratic, the differences of the differences will be equal.

d₂ − d₁ = 25.2 − 3.6 = 21.6

d₃ − d₂ = 176.4 − 25.2 = 151.2

d₄ − d₃ = 1234.8 − 176.4 = 1058.4

The differences of the differences are not equal, so this is not quadratic.

If the function is exponential, the ratios will be equal.

r₁ = y₁ / y₀ = 4.2 / 0.6 = 7

r₂ = y₂ / y₁ = 29.4 / 4.2 = 7

r₃ = y₃ / y₂ = 205.8 / 29.4 = 7

r₄ = y₄ / y₃ = 1440.6 / 205.8 = 7

The ratios are equal, so the function is exponential.