Select all the correct answers.A botanist plants an avocado seed and a peach seed and observes the heights of the trees over time.The graph shows the height, in inches, of the avocado tree.This function, where t represents the time in weeks, models the height, in inches, of the peach tree.𝑃⁡(𝑡)=3⁢ln⁡(2⁢𝑡+3)−5Which statements are true about this situation? The peach tree had a greater average rate of change between the 2nd and 6th weeks after being planted. The peach seed was planted closer to ground level. The peach tree will eventually be taller than the avocado tree. The avocado tree had a greater average rate of change between the 2nd and 6th weeks after being planted. The avocado seed was planted at ground level.

The graph shows the linear relationship between the height of a plant (in centimeters) and the time (in weeks) that the plant has been growing.Which statements are correct? Choose three correct answers.ResponsesThe rate of change is 1.The rate of change is 1 .The plant grows 4 cm in 1 week.The plant grows 4 cm in 1 week.The rate of change is 4141.The rate of change is 4 over 1.The plant grows 1 cm in 4 weeks.

During the early growth of a super-fast growing bamboo ‘Guadua Angustifolia’, found in Southern America andoften referred to as ‘Vegetal Steel’, the average height was measured (in mm) against the time (in days) afterobservations began. This was then modelled with the equation:H = 3e1.3t.Interpret the meaning of the ’3’ in the model’s equation.a)Calculate the height of the bamboo after 5 days.b)Calculate how much the plant grows during day 6, giving your answer to the nearest metre.c)Calculate the rate of increase of the plant at the start of day 6. Additionally, explain why this is differentto your answer to part (c).d)When graphing the data, explain why the researchers would have plotted ln(H) against t, rather thanln(H) against ln(t)e)Explain why the model may not be suitable for the lifetime of the bamboo. Use a suitable calculation tohelp

The height of a tree increased by 12%12% from 2022 to 2023. If the 2023 height is b𝑏 times the 2022 height, what is the value of b𝑏?

In the initial period of its life a particular species of tree grows in the manner described by the rule d=d010mt𝑑=𝑑010𝑚𝑡 where d𝑑 is the diameter (in cm) of the tree t𝑡 years after the beginning of this period. The diameter is 52 cm after 1 year, and 80 cm after 3 years. Calculate the values of the constants d0𝑑0 and m𝑚

A plant is 6.2 cm tall.The height of the plant increases by 11% each week.Find how tall the plant will be after two weeks.