Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.001618x4 + 0.057326x3 – 1.1367x2 + 11.46x + 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?

substitute x=2.5 or x=12 in the given formula and evaluate the function to get the human equivalent years.

For example,
f(2.5)=- 0.001618(2.5)^4 + 0.057326(2.5)^3 – 1.1367(2.5)^2 + 11.46(2.5) + 2.914

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so what is the answer to the problem

where is the answer to this problem

To find the age of a unicorn in human equivalent years when it is 2.5 years old, we substitute x = 2.5 into the formula f(x).

f(x) = -0.001618x^4 + 0.057326x^3 – 1.1367x^2 + 11.46x + 2.914

f(2.5) = -0.001618(2.5)^4 + 0.057326(2.5)^3 – 1.1367(2.5)^2 + 11.46(2.5) + 2.914

To calculate this, we need to evaluate the powers of 2.5 first:

(2.5)^4 = 2.5 * 2.5 * 2.5 * 2.5 = 39.0625
(2.5)^3 = 2.5 * 2.5 * 2.5 = 15.625
(2.5)^2 = 2.5 * 2.5 = 6.25

Substituting these values back into f(2.5):

f(2.5) = -0.001618(39.0625) + 0.057326(15.625) – 1.1367(6.25) + 11.46(2.5) + 2.914

Performing the calculations:

f(2.5) = -0.0632384375 + 0.89541275 – 7.1040625 + 28.65 + 2.914

f(2.5) = 24.2921110625

Therefore, when a unicorn is 2.5 years old, its age in human equivalent years is approximately 24.29 years.

To find the age in human equivalent years when the unicorn is 12 years old, we substitute x = 12 into the formula f(x).

f(x) = -0.001618x^4 + 0.057326x^3 – 1.1367x^2 + 11.46x + 2.914

f(12) = -0.001618(12)^4 + 0.057326(12)^3 – 1.1367(12)^2 + 11.46(12) + 2.914

Evaluating the powers of 12:

(12)^4 = 12 * 12 * 12 * 12 = 20736
(12)^3 = 12 * 12 * 12 = 1728
(12)^2 = 12 * 12 = 144

Substituting these values back into f(12):

f(12) = -0.001618(20736) + 0.057326(1728) – 1.1367(144) + 11.46(12) + 2.914

Performing the calculations:

f(12) = -33.528691648 + 99.087769472 – 164.05248 + 137.52 + 2.914

f(12) = -57.058401176

Therefore, when a unicorn is 12 years old, its age in human equivalent years is approximately -57.06 years.