SOLUTION: In a chemistry class, the students in lab derived a function to model the results of their experiment on the effect of heat on a chemical where x represents the number of minutes h

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Question 1204901: In a chemistry class, the students in lab derived a function to model the results of their experiment on the effect of heat on a chemical where x represents the number of minutes heat was applied at a constant temperature set by the lab instructions.
Their function was f%28x%29+=+16x%2F%28x%5E2%2B2%29. The teacher said the function should have been g%28x%29+=+12x%2F%28x%5E2%2B1%29.
a) Was there ever any time at which these two functions were the same. If so, when?
b) For what values of x is their derived function greater than the actual function?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+16x%2F%28x%5E2%2B2%29
g%28x%29+=+12x%2F%28x%5E2%2B1%29

a) Was there ever any time at which these two functions were the same. If so, when?
f%28x%29+=g%28x%29+
16x%2F%28x%5E2%2B2%29=+12x%2F%28x%5E2%2B1%29....cross multiply
16x%28x%5E2%2B1%29=+12x%28x%5E2%2B2%29
16x%5E3+%2B+16x=+12x%5E3+%2B+24x
16x%5E3+%2B+16x-12x%5E3+-+24x=0
4x%5E3+-+8x=0
4x+%28x%5E2-2%29=0
solutions:
x=0
x=sqrt%282%29
x=-sqrt%282%29

the functions are the same when x=0, x=sqrt%282%29, and x=-sqrt%282%29

b) For what values of x+is their derived function greater than the actual function?
16x%2F%28x%5E2%2B2%29%3E+12x%2F%28x%5E2%2B1%29
Solutions:
x%3Esqrt%282%29
-sqrt%282%29%3Cx%3C0
Interval notation:
(sqrt%282%29, infinity)
(-sqrt%282%29, 0)

see the graph:
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