# 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?

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 $y = x {\left(1 + 0.035\right)}^{10}$ or

$y = x {\left(1.035\right)}^{10} \approx 1.4106 \cdot x$

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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