The scatter plot drawn in the image below depicts the concentration, f, in milligrams per liter (mg/L), of an antibiotic in a patient’s bloodstream x hours after taking the antibiotic. Which of the following functions best describes the relationship shown ?
1) f(x) = 22.45x2+ 92.38x + 1.86 2) f(x) = -22.45x2+ 92.38x + 1.86 3) f(x) = 1.86(22.45)x 4) f(x) = 22.45(1.86)xSolution:
Choice B is correct.
If we join the points given, we know the curve will form a kind a parabola and not an exponential function.
The parabola is best represented by a quadratic equation.
So choices C and D are ruled out.
Furthermore, the parabola is opening downwards.
Therefore, the coefficient of x2 will be negative.Out of choices A and B, only choice B satisfies the given criteria.
Hence Choice B is the correct answer .
