Question

The number of trees of a given species per acre is approximated by the modelN = 2500(10^-0.12x), 3<=3<=30where x is the average diameter of the trees (in inches) 4.5 feet above the ground. Use the model to approximate the average diameter (in inches) of the trees in a test plot whenN = 22. (Round your answer to two decimal places.)inNeed Help?Read ItWatch ItSubmit Answer

Answer 1

We have the next equation:

`N=2500\cdot(10^(-0.12x)),3\leq x\leq30`

For N = 22, we have:

`_{}22=2500\cdot(10^(-0.12x))=(22)/(2500)=10^(-0.12x)`

We need to use the concept of the logarithm to find x. Then:

`0.0088=(10^(-0.12x)_{})\Rightarrow\log (0.0088)=\log (10^(-0.12x)_{})=-0.12x\cdot\log (10)`

Then

`\log (0.0088)=-0.12x\cdot1\Rightarrow x=(\log (0.0088))/(-0.12)\Rightarrow x=(-2.0555)/(-0.12)\Rightarrow x=17.1291`

Then, the value for x = 17.13 (rounding to two decimal places). This is the solution to the equation.