How to reduce steepness of logistic curve?

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I am simulating an assay with the following equation: $$y = xd(1 - \frac{x}{k})$$ where $d$ is the duplication time and $k$ is the asimptote. However, the simaluted curve (in red) is too steep compared to the actual data (green and blue): enter image description here Is there a way to reduce the 'steepness' of the curve? I tried with a lower duplication value but it only translates the data, not the curve. Same thing with k.

Thank you.