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 $G (t) = \frac{18.72}{1 + 5 e^{- 2.2 t}}$ , where $G$ is the height of the plant in centimeters and $t$ is the time in weeks. Describe how the species grows over the first $6$ weeks of life by drawing the graph of $G^{'} (t)$ using a graphing utility.

Accepted Answer

The plant starts growing quickly and reaches its fastest point when $t=0.73$ weeks. After $t=0.73$ 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 $t=0.73$ weeks. After $t equals 3$ 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 $G (t) = \frac{18.72}{1 + 5 e^{- 2.2 t}}$ weeks. After $t equals 2$ 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 $G (t) = \frac{18.72}{1 + 5 e^{- 2.2 t}}$ weeks. After $t equals 2$ 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.

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