# Question: the population of pine trees in a forest region is...

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The population of pine trees in a forest region is infected by a needle blight fungus that kills off trees, so that the number of trees decreases with time. Suppose that n(t) is the number of pine trees in the region at time t (in years). Initially (at time t = 0) there are 8000 trees. Assume that the number of pine trees is modelled by the exponential decay function n(t) = 8000e kt (t ≥ 0), where k is a constant. After 3 years, 6000 trees remain. (a) Find the value of the constant k, correct to three significant figures. How long will it take for the number of trees to reduce to 3000? Give your answer in years to one decimal place.