algebra 2………help………?
2)Suppose the intial height from which a rubber ball drops is 100in. The rebound heights to the nearest inch are 80, 64, 51, 41…
a) what is the rebound ratio for this ball?
b) what is the height of the tenth rebound?
c) after how many bounces will the ball rebound less than1in?less than0.1in?
Favorite Answer
80 in / 100 in = 4/5 (or 0.8)
b) what is the height of the tenth rebound?
h(n) = h(orig) * (rebound ratio) ^n
h(10) = 100 * (0.8)^10 = 100 * 0.1073741824 = 10.74 in (approx)
c) after how many bounces will the ball rebound less than1in?
h(n) > h(orig) * (rebound ratio) ^n
1 in < 100 in * (0.8) ^n 1/100 < 0.8^n 0.01 < 0.8^n n > log[base 0.8](0.01)
n > log(0.01) / log(0.8)
n > 20.64
After 21 bounces.
less than0.1in?
h(n) = h(orig) * (rebound ratio) ^n
0.1 in < 100 in * (0.8) ^n 1/1000 < 0.8^n 0.001 < 0.8^n n > log[base 0.8](0.001)
n > log(0.001) / log(0.8)
n > 30.96
After 31 bounces.
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