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A tree grows 2.80 m during the first year since it was planted. During each subsequent year, the tree's growth is 85% of its growth the previous year. Determine the first year in which the growth of the tree is less than half a metre. 

 Jun 4, 2021
 #1
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We need  to  solve  this  for  n

 

2.8 ( .85)^(n - 1)   =   .5

 

(.85)^(n - 1)  = .5/2.8

 

(.85)^(n - 1)   =  5/28        take the log of both sides

 

log (.85(^(n - 1)  = log (5/28)        and by a log property we can wite

 

(n - 1)  log (.85)  =  log (5/28)

 

n - 1   =  log (5/28) /log (.85)

 

n =   log (5/28) / log (.85)  +  1   ≈  11.6 yrs

 

So  about the 12th year

 

 

cool cool cool

 Jun 4, 2021

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