The volume of harvestable timber in a young forest grows exponentially with a yearly rate of increase equal to 3.5%. What percentage increase is expected in 10 years?

1 Answer
Jun 28, 2018

#41%# increase in volume of timber is expected in #10# years.

Explanation:

Let the initial volume of timber be #x#

Growth rate per year is #r=3.5%=3.5/100=0.035#

Final volume equation of timber is #y=x(1+r)^t ; t # is number of

years. Final volume after #10# years is #y=x(1+0.035)^10 # or

#y=x(1.035)^10 ~~ 1.4106 *x #

Percentage increase in #10# years is #y%= (1.4106 x-x)/x*100#

#:. y%= (cancel x(1.4106-1))/ cancel x*100= 41.06%#

#41%# increase in volume of timber is expected in #10# years.

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