A non-native species of fish is introduced into a lake and is attacking a certain type of native species of fish. The following functions model the populations of the two species of fish for 0 ≤ t ≤ 9 where t is the number of months since the fish was introduced. Native: x(t) = −447.94t3 − 5250t2 + 44992t + 150000 Non-native: y(t) = −589.14t3 − 0.7t2 + 5994t + 20 (a) Will the native species survive 9 months. Why or why not? (b) When, in the nine months, will the population of the native species reach a maximum? (c) When, in the nine months, will the population of the non-native species reach a maximum?

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