Asked by Anonymous

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.

a) Calculate to the nearest 0.001m, the growth of the tree in the fourth year.

Tn = ar^n-1
T4 = 2.80(0.85)^10-1
T4 = 2450
I don't get how to do this, the answer is wrong, its supposed to be 1.72m :\

Determine the first year in which the growth of the tree is less than half a metre.

Answers

Answered by Reiny
Where in the world did you get 10 in the 10-1
should have been 4-1

T4 = 2.8(.85)^3 = 1.719 or 1.72

for growth to be .5

.5 = 2.8(.85)^(n-1)
divide by 2.8
.17857.. = .85^(n-1)
take log of both sides
log (.17857..) = log [.85^(n-1)]
log (.17857..) = (n-1)log [.85]
n-1 = log (.17857..) / log [.85] = 10.6
n = 11.6

in year 11, growth = 2.8(.85)^10 = .5512
in year 12, growth = 2.8(.85)^11 = .468

so what do you think?
Answered by Anonymous
So that would be Year 12.
Answered by Reiny
yes
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions