Mathematical Modeling Homework

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 thispart).(b) By looking at first or second differences, indicate whether the graph is likely tobe linear.(c) By looking at first or second differences, indicate whether the graph is likely tobe 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 groundagain.12. 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 thispart).(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 forwhich insurance rates hit their minimum (some error will be introduced in thisstep; so do your best to be accurate).23. Enraged about the results of their first test, a student tosses their calculator off a 2mile high cliff. Suppose that it hits the ground in 1 minute; it is tossed from a heightof 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 aquadratic equation, i.e. an equation of the form:h(t) = at2 + bt + cUsing the information in the problem, set up (but do not solve) a system ofequations 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 functionof time (your answer should be a quadratic equation!)