M106 Practice Exam 1

[Note: This was Exam 1 given September 19, 1995, in Math 106.]

Instructions: Show all of your work and clearly explain your answers. This is particularly important on problems with a numerical answer, to allow the possibility of partial credit. No books are allowed during the exam, but you may use your calculator.

Problem [1] (8 pts) Suppose the Big Muddy Water Co. charges its customers $10.00 a month plus $2.00 per 100 gallons of monthly water usage.
Problem [2] (9 pts) The table gives some values for two functions, f(x) and g(x), one of which is linear, the other exponential.
Problem [3] (8 pts) The graph of y = x2 is shifted up one unit, then right 2 units, then reflected across the x-axis, to give the graph of y = f(x).
Problem [4] (7 pts) Suppose you take a 5 hour trip by car, stopping once, to eat lunch. Let d = f(t) be the distance covered during the trip as a function of time t, where t is the number of hours since the trip started.
Problem [5] (7 pts) Bank A offers a savings account with an 8.3% annual interest rate, compounded daily. Bank B offers a savings account with an 8.4% annual interest rate, compounded twice a year, and Bank C offers a savings account with an 8.5% annual interest rate, compounded continuously. Which bank offers the best deal and which offers the worst deal? Explain how you decided.

Problem [6] (11 pts) A sinusoidal function y = f(x) and a polynomial y = g(x) are graphed below. Graph goes here. Graph goes here.