Question to test your Product and Quotient Rules knowledge

Question

The growth of a certain plant species over time can be modeled by the function G(t)=18.721+5e−2.2tG\left(t\right)=\frac{18.72}{$$1+5e^{-2.2t}$$}, where GG is the height of the plant in centimeters and tt is the time in weeks. Describe how the species grows over the first 66 weeks of life by drawing the graph of G′$$(t)G^{\prime}(t) $$using a graphing utility.

Accepted Answer

The plant starts growing quickly and reaches its fastest point when t=0.73t=0.73 weeks. After t=0.73t=0.73 weeks, the growth continues but at a slower pace. Approaching week 6 and beyond, the growth rate approaches zero, indicating the plant is nearing its maximum height.

Answer

The plant starts growing quickly and reaches its fastest point when t=0.73t=0.73 weeks. After t=3t=3 weeks, the growth continues but at a slower pace. Approaching week 6 and beyond, the growth rate approaches zero, indicating the plant is nearing its maximum height.

Answer

The plant starts growing quickly and reaches its fastest point when t=2t=2 weeks. After t=2t=2 weeks, the growth continues but at a slower pace. Approaching week 6 and beyond, the growth rate approaches zero, indicating the plant is nearing its maximum height.

Answer

The plant starts growing quickly and reaches its fastest point when t=4t=4 weeks. After t=4t=4 weeks, the growth continues but at a slower pace. Approaching week 6 and beyond, the growth rate approaches zero, indicating the plant is nearing its maximum height.

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