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A forest has pine trees, but a disease is introduced that kills of the pine trees in the forest every year.Write a function that gives the number of pine trees remaining in the forest years after the disease is introduced.
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Q. A forest has pine trees, but a disease is introduced that kills of the pine trees in the forest every year.Write a function that gives the number of pine trees remaining in the forest years after the disease is introduced.
- Understand Decay Pattern: Step : To write the function, we need to understand the pattern of decay of the pine trees. Since one quarter of the trees are killed each year, this means that each year, the forest retains three quarters (or ) of its pine trees from the previous year. This is a geometric decay with a decay factor of (since ).
- Exponential Decay Function: Step : The general form of an exponential decay function is , where is the initial quantity and decay\_factor is the factor by which the quantity decreases each year. In this case, is the initial number of pine trees, which is , and the decay factor is .
- Substitute Values: Step : Substitute the values into the exponential decay function to get the specific function for this problem. . This function will give us the number of pine trees remaining in the forest years after the disease is introduced.
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