A hedgehog population on a small island off the coast of Ireland is approximated by 1647...

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A hedgehog population on a small island off the coast of Ireland is approximated by 1647 where t is measured in years since 1990. 1+e4.5-0.3t P(t) : = 1. What happens to the population as t → ∞? Interpret this result in biological terms. 2. Estimate when the hedgehog population was growing most rapidly; that is, find when P'(t) is maximized. How large was the population at this time? 3. Use your answers from parts (1) and (2) along with information about the first and second derivatives to sketch P. What natural causes may explain the shape of the graph of P. A hedgehog population on a small island off the coast of Ireland is approximated by 1647 where t is measured in years since 1990. 1+e4.5-0.3t P(t) : = 1. What happens to the population as t → ∞? Interpret this result in biological terms. 2. Estimate when the hedgehog population was growing most rapidly; that is, find when P'(t) is maximized. How large was the population at this time? 3. Use your answers from parts (1) and (2) along with information about the first and second derivatives to sketch P. What natural causes may explain the shape of the graph of P.