The single-step error of Heun's method scales as . In 3-4 sentences, explain what this statement means. Include an example.

You have the following 10 data points recorded in an experiment (x is the independent variable and y is the dependent variable):

You decide to use the built-in Python function nppoly.polyfit() to fit the data with a 9th order polynomial, using the input: p = nppoly.polyfit(x,y,9).

a) Find the value of  for this fit. Give your answer to 2 decimal places.

b) Explain/interpret your  value from the previous question (1 sentence).

c) These data points describe the percentage of surveyed people, y, who have been to the dentist within the last x years. Discuss your interpretation of the fit and what it means for interpolated and/or extrapolated values using this function. Explain your reasoning (2-4 sentences).

Describe two different aspects between closed (bracketed) and open root-finding methods.

For loops and while loops both repeat a set of instructions. Explain the difference between the two loop types. Also, describe when you would use one type over the other.

Copy/paste your code for all parts of the previous question into the textbox below to receive method marks

Copy/paste your code for all parts of the previous question into the textbox below to receive method marks.

Which statement below is true about the midpoint method and Heun’s method for solving ordinary differential equations?

Consider a CSV file, data.csv, that contains data about a grocery store's inventory. The dataset contains 3 attributes and many observations. A sample of this dataset is shown below:

In order to fit an exponential model, , to a set of data, the points in the dataset first need to be transformed. A linear relationship should be seen when you plot: