Select the correct answer. The height that a properly inflated basketball bounces decreases exponentially by 27.8% with each subsequent bounce after the initial drop.A local basketball league tests the inflation of their basketballs by dropping them from a height of 6 feet. Which equation can be used to model the height of the basketball,H, after bbounces? A. H=6(0.722)^b B. H=6(1.278)^b C. H=6(0.278)^b D. H=6(0.9722)^b

To determine the correct equation to model the height of the basketball after \( b \) bounces, we need to consider the exponential decrease in height with each bounce.<br /><br />The problem states that the height decreases by 27.8% with each bounce. This means that the basketball retains 100% - 27.8% = 72.2% of its height after each bounce.<br /><br />Therefore, the factor by which the height is multiplied after each bounce is 0.722 (since 72.2% as a decimal is 0.722).<br /><br />The initial height from which the basketball is dropped is 6 feet. Thus, the equation modeling the height \( H \) after \( b \) bounces is:<br /><br />\[ H = 6(0.722)^b \]<br /><br />So, the correct answer is:<br /><br />A. \( H = 6(0.722)^b \)