Question

question attempt: 1 of unlimited
$y = -12.5x^{2} + 254x + 1225$
$y = -6.2x^{2} + 207x + 2080$
$y = -15.9x^{2} + 403x + 614$
(a) which curve fits the data best?
$circ$ figure 1 $circ$ figure 2 $circ$ figure 3
(b) use the equation of the best fitting curve from part (a) to predict the volume of the plant when it has been given 16 milligrams of fertilizer. give an exact answer, not a rounded approximation.
$square$ cubic centimeters

Explanation:

Step1: Evaluate curve fit accuracy

Visually compare the three figures: Figure 3's curve passes closest to all data points, matching the trend best.

Step2: Substitute x=16 into Figure3's equation

Use $y = -15.9x^2 + 403x + 614$, replace $x$ with 16.
First calculate each term:
$15.9\times16^2 = 15.9\times256 = 4070.4$
$403\times16 = 6448$

Step3: Compute final y value

$y = -4070.4 + 6448 + 614$

Answer:

(a) Figure 3
(b) 2991.6 cubic centimeters