Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.001518x4 + 0.067326x3 – 1.4367x2 + 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 can substitute the given age values into the formula f(x) = -0.001518x^4 + 0.067326x^3 – 1.4367x^2 + 12.46x + 2.914.

1. When a unicorn is 2.5 years old:
Substitute x = 2.5 into the formula:
f(2.5) = -0.001518(2.5)^4 + 0.067326(2.5)^3 – 1.4367(2.5)^2 + 12.46(2.5) + 2.914.

Calculate the expression:
f(2.5) = -0.001518(39.0625) + 0.067326(15.625) – 1.4367(6.25) + 12.46(2.5) + 2.914.

f(2.5) ≈ -0.05931 + 1.04945625 – 9.041875 + 31.15 + 2.914.

f(2.5) ≈ 26.01327.

Therefore, when a unicorn is 2.5 years old, its age in human equivalent years is approximately 26.01327 years.

2. When a unicorn is 12 years old:
Substitute x = 12 into the formula:
f(12) = -0.001518(12)^4 + 0.067326(12)^3 – 1.4367(12)^2 + 12.46(12) + 2.914.

Calculate the expression:
f(12) = -0.001518(20736) + 0.067326(1728) – 1.4367(144) + 12.46(12) + 2.914.

f(12) ≈ -31.459328 + 116.156848 + (-206.928) + 149.52 + 2.914.

f(12) ≈ 29.20252.

Therefore, when a unicorn is 12 years old, its age in human equivalent years is approximately 29.20252 years.