question archive Steph Curry makes a three-point shot just before halftime of a basketball game
Steph Curry makes a three-point shot just before halftime of a basketball game
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Steph Curry makes a three-point shot just before halftime of a basketball game. The shot goes through the 10 foot tall net, and since it is halftime, nobody is around to collect it. Every time the ball bounces, it rebounds to 75% of its original height.
a) What is the height of the ball after it has bounced 4 times?
b) How long would it take for the height of the ball to be 1 foot?
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Answer:
a. = 3.1641 foot tall
b. = 8 times
Step-by-step explanation
a. The height of the ball after it has bounced 4 times is given by:
A = P * (r)n
where P is initial height = 10 feet, r is decay factor = 0.75, n is number of bounces = 4
therefore, A is given by:
A = 10 (0.75)4
= 3.1641 foot tall
b. Time taken for the height of the ball to be 1 foot is given by:
A = 10 (0.75)n
therefore, n is given by:
1 = 10 (0.75)n
(0.75)n = 0.1
n log 0.75 = log 0.1
n = log 0.1/log 0.75
= 8.0039
= 8 times
