MAP4C – Unit 1 – Mathematical Modelling Name: ______
ASSIGNMENT (Activity 4): CLASSIFYING MATHEMATICAL MODELS
Be sure to show all work. You don’t have to submit your graphs, but you need to save your Excel file and submit it to the teacher.
1. Determine what type of relationship (linear, quadratic, exponential, or neither) exists in each case. Justify your answer. [8]
2. Sara invests $1000 into a fund that earns compound interest. This means that as interest is earned, the interest is added to the original principal, so that the next interest amount is calculated on a higher value. The following table shows the value of Sara’s investment after each year.
a) Complete first difference and ratio columns to verify that this is an exponential relationship. [3]
b) Using the ratio value obtained, what is the interest rate of the investment? [1] ______
c) Use technology to determine the regression equation. [3] ______
d) Use the regression equation to find the value of Sara’s investment after a total of 25 years. [2]
3. The following table shows the concentration of medication in a patient’s blood after an injection.
a) Which model (linear/quad/exponential) is the most appropriate for this example? [1] ______
b) Use technology to determine regression equation. [3]
______
c) Use the regression equation to find the concentration after 3 hours. What can you conclude from your answer? [3]
4. The following table shows the number of internet hosts (computers that store web pages) since 1993.
a) Use technology to determine both quadratic and exponential regression equations. (Hint: Use 1993 = year 0, 1994 = year 1, etc). [6]
Quadratic: ______
Exponential: ______
b) Use both regression equations to predict the number of internet hosts in the year 2020. Which equation do you think gives a more reasonable result? Use characteristics of the graph and R2 values to explain. [4]