Resource Management Wood is a sustainable, renewable, natural resource when you manage forests properly. Your lumber company has 1,200,000 trees. You plan to harvest 7% of the trees each year. How many years will it take to harvest half of the trees?
Know | Need | Plan |
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Number of years it takes to harvest 600,000 trees |
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What equation should you use to model this situation? Since you are planning to harvest 7% of the trees each year, you should use
Step 1 Is an exponential model reasonable for this situation?
Yes, you are harvesting a fixed percentage each year.
Step 2 Define the variables and determine the model.
Let
Let T(n) = the number of trees remaining after n years.
A reasonable model is
Step 3 Use the model to write an exponential equation.
So,
Step 4 Solve the equation. Use logarithms.
It will take about 9.55 years to harvest half of the original trees.
A logarithmic equation is an equation that includes one or more logarithms involving a variable.