Final answer:
Without specific growth data or the function h(t), it's impossible to determine the growth pattern, initial height, or exact time Pooja's plant took to reach maximum height. The plant's life span is influenced by environmental conditions, water, nutrients, and genetics.
Step-by-step explanation:
The question you have asked pertains to the growth pattern of Pooja's plant, its initial height, the time it took to reach its tallest height, and factors affecting the plant's life span. Unfortunately, without specific data on the function h(t) or additional information on the growth rates, it is impossible to provide a factual answer to parts (a), (b), and (c) of your question. Generally in biology, the growth pattern of plants can be influenced by factors such as sunlight, water, soil nutrients, and conditions.
For part (d), the factors affecting a plant's lifespan can include environmental conditions, water availability, nutrient supply, and genetic factors. Plant life spans can range from a few weeks to thousands of years, depending on the species and conditions.
In experiments like those described in your additional information, controlled variables such as light exposure, soil content, and watering are changed to determine their effect on plant growth. Potential flaws in experimental designs can impact the validity of conclusions, such as the differing conditions of sunlight in the detergent experiment.