mathematical modeling homework
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1. Below is a table of the heights of a rocket over time: (a) Create a scatter plot of the data (you do not need to turn in anything for this part). (b) By looking at first or second differences, indicate whether the graph is likely to be linear. (c) By looking at first or second differences, indicate whether the graph is likely to be quadratic. (d) Find a quadratic regression for the above data; list your equation with all coefficients up to two decimal places. (e) Using your answer to the previous part, estimate when the rocket hits the ground again. 1 2. The following table gives the average yearly car insurance rates for varying ages. (a) Create a scatter plot of the data (you do not need to turn in anything for this part). (b) Find a quadratic regression for the above data; list your equation with all coefficients up to two decimal places. (c) Using your answer to the previous part, estimate to the nearest year the age for which insurance rates hit their minimum (some error will be introduced in this step; so do your best to be accurate). 2 3. Enraged about the results of their first test, a student tosses their calculator off a 2 mile high cliff. Suppose that it hits the ground in 1 minute; it is tossed from a height of 2 miles; and in half a minute, it is at a height of 5/4 or 1.25 miles. (a) Assume that the height of the calculator as a function of time is modeled by a quadratic equation, i.e. an equation of the form: h(t) = at2 + bt + c Using the information in the problem, set up (but do not solve) a system of equations which will allow us to solve for a, b and c. (b) Using the previous part, find the function h(t) which models height as a function of time (your answer should be a quadratic equation!)
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