The Utopian Tree goes through 2 cycles of growth every year. Each spring, it doubles in height. Each summer, its height increases by 1 meter.A Utopian Tree sapling with a height of 1 meter is planted at the onset of spring. How tall will the tree be after growth cycles?For example, if the number of growth cycles is , the calculations are as follows:Period Height0 11 22 33 64 75 14Function DescriptionComplete the utopianTree function in the editor below.utopianTree has the following parameter(s):int n: the number of growth cycles to simulateReturnsint: the height of the tree after the given number of cyclesInput FormatThe first line contains an integer, , the number of test cases. subsequent lines each contain an integer, , the number of cycles for that test case.ConstraintsSample Input3014Sample Output127ExplanationThere are 3 test cases.In the first case (), the initial height () of the tree remains unchanged.In the second case (), the tree doubles in height and is meters tall after the spring cycle.In the third case (), the tree doubles its height in spring (, ), then grows a meter in summer (, ), then doubles after the next spring (, ), and grows another meter after summer (, ). Thus, at the end of 4 cycles, its height is meters.

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 already 41 centimeters tall, and it will grow one centimeter every month.Let H be the plant's height (in centimeters) after M months.Write an equation relating H to M. Then use this equation to find the plant's height after 12 months.

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 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?

At the beginning of spring, Nolan planted a small sunflower in his backyard. The graph below represents the sunflower's height in inches after xx weeks. What does the slope of the line represent?123451013.51720.52427.53134.53841.50xy0∙Height (inches)Time (weeks)AnswerMultiple Choice AnswersHow much the sunflower grows, in inches, each week.A height of 13.5 inches after one week.The sunflower's height after 0 weeks.The sunflower's final height