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12-35.

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 .