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- grab unlimited access to millions of moviesâdownload, stream, and never payQuestion: A plant biologist is modeling the growth of a genetically modified crop using the function \( G(t) = t - rac{t^2}{4} \), where \( t \) represents time in weeks. If \( b_n \) is defined recursively by \( b_1 = 1 \) and \( b_{n+1} = G(b_n) \), compute \( \lim_{n o \infty} b_n \).
- Solution: We are given a recursive sequence defined by \( b_{n+1} = G(b_n) \), where \( G(t) = t - rac{t^2}{4} \), and \( b_1 = 1 \). We are to find \( \lim_{n o \infty} b_n \), assuming the limit exists.
- Let \( L = \lim_{n o \infty} b_n \). Since \( b_{n+1} = G(b_n) \), taking limits on both sides gives:
