RIP Tree
Shortly after a tree reaches its maximum height of a species of bugs which feed on the tree begin to breed on it. The rate of increase in the number of bugs at any point in time is proportional to the number of bugs present at that time. The rate of the tree's shrinkage is also proportional to the number of bugs present at that time.
How many months will it take for the tree to disappear? Enter your answer to 3 significant figures.
Details and Assumptions:
- Initially, there exist 10 bugs, which produce 100 more bugs in the first six months.
- When the bug population reaches 300, the tree is shrinking at a rate of per month.
The answer is 13.5.
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