Essay; show all work. Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.011718x4 + 0.187326x3 – 1.3367x2 + 12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old?

F(x) = Y.

(X,Y) = (2.5,28.2), (12,40.7).

Essay show all work. Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.011718x4 + 0.187326x3 – 1.3367x2 + 12.46x + 2.914.When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old?

To find the age of a unicorn in human equivalent years, we will use the provided formula: f(x) = - 0.011718x^4 + 0.187326x^3 – 1.3367x^2 + 12.46x + 2.914.

Let's substitute the given ages into the formula to find the unicorn's age in human equivalent years.

1. When the unicorn is 2.5 years old:
To find its age, substitute x = 2.5 into the formula:
f(2.5) = - 0.011718(2.5)^4 + 0.187326(2.5)^3 – 1.3367(2.5)^2 + 12.46(2.5) + 2.914.

Calculating these values, we get:
f(2.5) = -0.011718(39.0625) + 0.187326(15.625) – 1.3367(6.25) + 12.46(2.5) + 2.914.

f(2.5) = -0.45703125 + 2.9267125 – 8.354375 + 31.15 + 2.914.

f(2.5) ≈ 28.179.

Therefore, when the unicorn is 2.5 years old, its age in human equivalent years is approximately 28.179 years.

2. When the unicorn is 12 years old:
Similarly, substitute x = 12 into the formula:
f(12) = - 0.011718(12)^4 + 0.187326(12)^3 – 1.3367(12)^2 + 12.46(12) + 2.914.

Calculating these values, we get:
f(12) = -0.011718(20736) + 0.187326(1728) – 1.3367(144) + 12.46(12) + 2.914.

f(12) = -242.71 + 324.415 + (-192.589) + 149.52 + 2.914.

f(12) ≈ 41.57.

Therefore, when the unicorn is 12 years old, its age in human equivalent years is approximately 41.57 years.

In conclusion, when the unicorn is 2.5 years old, its age in human equivalent years is approximately 28.179 years, and when it is 12 years old, its age in human equivalent years is approximately 41.57 years.