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)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 x2 will be negative.

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

Hence Choice B is the correct answer .