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 b bounces?

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58