Answer:
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.
