**14. At a 15 percent annual inflation rate, the value of the dollar would decrease by approximately one-half every 5 years. At this inflation rate, in approximately how many years would the dollar be worth 1/1,000,000 of its present value?**

A) 25

B) 50

C) 75

D) 100

E) 125

Answer (D)

So, I put D down when taking this but the way I got the answer was a little less then desired. I approximated log_2(100) ~ 20 which took me awhile. I was wondering how you guys did this. I remember there being a function to tell you this answer but I forget the exact expression.

**24. If A and B are events in proabability space such that 0 < P(A) = P(B) = P(A Intersect B) < 1, which of the following CANNOT be true?**

A) A and B are independent.

B) A is a proper subset of B.

C) A != B

D) A intersect B = A union B

E) P(A)P(B) < P(A Intersect B)

Answer (A)

I got this wrong, I have never taken a class dealing with proabability spaces so I may just not have enough tools at my disposale. But if anyone could explain this to me I would appreciate it.

**31. If**

f(x) =

Root( 1 - x^2) for 0</= x </=1

x-1 for 1 < x </= 2

f(x) =

Root( 1 - x^2) for 0</= x </=1

x-1 for 1 < x </= 2

then the Integral from 0 to 2 of f(x) dx is?

A) pi/2

B) Root(2)/2

C) 1/2 + pi/4

D) 1/2 + pi/2

E) Undefined

So, I started by spliting the integral from 0 to 1 and then 1 to 2. My problem is that I was unsure how to integrate Root(1-x^2) I used integration by parts with little to no help.

**43. Let n be an integer greater than 1. Which of the following conditions guarantee that the equation x^n = Sum from i=0 to n-1 of a_i x^i has at least one root int he interval (0,1)?**

I. a_0 > 0 and Sum i=0 to n-1 of a_i < 1

II. a_0 > 0 and Sum i=0 to n-1 of a_i > 1

III. a_0 < 0 and Sum i=0 to n-1 of a_i > 1

A) None

B) I Only

C) II Only

D) III Only

E) I and III

Answer (E)

So, I was sure that this problem had to do with the two expressions

Sum of the roots = (-1)^n * -a_(n-1)

Product of the roots = a_0

But I'm unsure how their conditions imply the root is between 0 and 1.