(c) We have a system of linear equations in five variables that is set up in the matrix equation AX = B. A looks like 1000 0 20 A= 0 0 010 00 0 0: DO0 0 How many solutions does this system have? Justify your answer. Hint: This is not an augmented matrix. (d) You invest $3,000 dollars into a CD that gives continuously compounded interest. However, the bank lied to you about the interest rate of 25%%. You see that you have $4,500 dollars in the CD after 2 years. Determine your real interest rate. (e) If you get a grade of by on a test today, a certain model says your grade I after f months of not reviewing the material is log ! = log -03log(f +1) Determine the grade you would get if you took the test four months from now (hint: solve for 1, then treat that as a function f(f).)(f) Suppose you are asked to solve a system of linear equations. You find that you get two different and unique solutions (11,1/1,21) and (12. 12,22). Assuming your work is correct, how many total solutions does this system of linear equations have? Justify your answer. (g) The rational function f(x) = x + has end behavior that looks like the function y = 17. Justify this based on what you know from this class (there are two possible reasons). (h) Determine a function f(x) that includes e and has x-intercept (3, 0). (i) Draw a graph with 4 local minimums and one r-intercept.10. Medium-length problems Answer the following. (a) Given two arbitrary functions f(x) with domain A and g (x) with domain B: i. Does fog always have the domain AnB? If not, give a counterexample. ii. If f (x) is one-to-one and g(x) is one-to-one, is f (x) + g(x) always one to one? If not, give a counterexample. (b) We are familiar with end behavior for polynomials. Now if f (x] is a polynomial, does the func- tion (x) = f(x) x- 1 always share the same end behavior as f(x)? Justify your