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) = 22.45x^{2}+ 92.38x + 1.86

2) f(x) = -22.45x

^{2}+ 92.38x + 1.86

3) f(x) = 1.86(22.45)

^{x}

4) f(x) = 22.45(1.86)

^{x}

Solution:

**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 x^{2}will be negative.

Out of choices A and B, only choice B satisfies the given criteria.

Hence Choice B is the correct answer .