Question

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?

Answer 1

`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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