SOLUTION: Leptin is a hormone that has a central role in fat metabolism. One study published in the New England Journal of Medicine measured serum leptin concentrations versus the percentage

Question 1009501: Leptin is a hormone that has a central role in fat metabolism. One study published in the New England Journal of Medicine measured serum leptin concentrations versus the percentage of body fat for 275 individuals. The concentration of leptin c (in ng/mL) is approximated by c = 219x2 − 26.7x + 1.64, where x is percentage of body fat.
a.Determine the concentration of leptin in an individual with 22% body fat (x = 0.22). Round to 1 decimal place.

b.If an individual has 3 ng/mL of leptin, determine the percentage of body fat. Round to the nearest whole percent.

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
a) From c = 219x^2 − 26.7x + 1.64
we plug in x = .22 and get a value for c...
c = 219(.22)^2 - 26.7(.22) + 1.64
c = 6.37 ng/mL
For part b, we work backwards, setting c = 3 and solving for x...
3 = 219x^2 − 26.7x + 1.64
x = .16 = 16% (solved by quadratic formula or calculator)
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