**Unformatted text preview: **to eat other destructive insects. If she were to use a pesticide, the growth rates would then become dx dt = x (1-y )-sx, dy dt = y ( x-1)-sy. ( * ) where s ≥ 0 is a measure of the “strength” of the pesticide – the larger the s , the stronger the pesticide. Currently there are only two commercially available strengths: s = 0 . 5 and s = 0 . 75. Plot the trajectories for the new system of equations ( * ) with these values of s . Will the aphids ever be totally eliminated? 3. If she knows her crops will survive if the aphid population never exceeds 2 . 6 million, which strength (if any) would you recommend she use: s = 0 . 0 (no pesticide), s = 0 . 5, s = 0 . 75? 4. By special permission, she could get a pesticide with the maximum strength of s = 1 . 5. Plot this trajectory. What happens to the ladybugs and aphids if she uses this pesticide?...

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