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The diagram at right shows a slope field. 

  1. Explain why must be a function of both and .

    Are the slopes in the diagram parallel anywhere?

  2. Sketch a solution curve that passes through the point .

    Your curve should look like a bell-shaped curve with a maximum at and a horizontal asymptote of .

  3. The slope field is for the differential equation . Write the equation of your solution curve.

    Once you integrate you should have a '. Use the point to solve for the value of .

Each quadrant has 5 rows of 5 short tangent segments, in second quadrant, each row has following changing slopes, from left to right, for given y values: @ 4.5, almost vertical, to 3, @ 3.5, almost vertical, to  2, @ 2.5, almost vertical, to  1.5, @ 1.5, almost vertical, to1, @ 0.5, slope of 3 changing to 0.5, each quadrant is a reflection of the adjacent quadrant over its respective axes. Your teacher will provide you with a model.