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A ball bounces back up \(\frac{2}{3}\) of the height from which it falls. If the ball is dropped from a height of 243 cm, after how many bounces does the ball first rise less than 30 cm?

 Oct 15, 2019
 #1
avatar+104969 
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We need to solve this

 

243 (2/3)^x  = 30  divide both sides by 243

 

(2/3)^x  =  30/243

 

(2/3)^x =  10/81       tak the log of both sides

 

log(2/3)^x  =  log (10/81)       and we can write

 

x log(2/3)  =  log (10/81)  divide both sides by  log(2/3)

 

x  =  log (10/81) / log(2/3)  ≈  5.16  =  after the 6th bounce

 

Check:

After the 5th bounce the ball will rise  to  243(3/4)^5  =   32 cm

After the 6th bounce the ball will rise to   243(2/3)^6 = 21.3 cm

 

cool cool cool

 Oct 15, 2019

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