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.