One problem in timber management is to determine how much of an area to leave uncut so that the harvested area is reforested in a certain period of time. It is assumed that reforestation takes place at a known rate per year, depending on climate and soil conditions. A reforestation equation expresses this growth as a function of the amount of timber standing and the reforestation rate. For example, if 100 acres are left standing after harvesting and the reforestation rate is 0.05, then 100 + (0.05 · 100), or 105 acres, are forested at the end of the first year. At the end of the second year, the number of acres forested is 105 + (0.05 · 105), or 110.25 acres.
Modify the program developed in Problem so that the user can enter a number of acres and the program will determine how many years are required for the number of acres to be completely reforested.
Problem
One problem in timber management is to determine how much of an area to leave uncut so that the harvested area is reforested in a certain period of time. It is assumed that reforestation takes place at a known rate per year, depending on climate and soil conditions. A reforestation equation expresses this growth as a function of the amount of timber standing and the reforestation rate. For example, if 100 acres are left standing after harvesting and the reforestation rate is 0.05, then 100 + (0.05 · 100), or 105 acres, are forested at the end of the first year. At the end of the second year, the number of acres forested is 105 + (0.05 · 105), or 110.25 acres.
Assume that the area has a total of 14,000 acres, with 2500 acres uncut and a reforestation rate of 0.02. Print a table showing the number of acres forested at the end of each year, for a total of 20 years.
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