i need help please help?

Question

ive got three questions and do not understand them do you know the answers 1. the bid $100 and increases 50% evry minute in how many minutes will the bid go over $2,500

2.sharon uses her initials, SLF, for her password. How many different three-letter passwords can she make with these letters

3.3. In how many ways can you make 45¢ in change using only nickels, dimes, and quarters.

Answer 1

PROBLEM 1:

Let t be the time

Bid at time t is a geometric sequence:
b(t) = b(0) * (1.5)t

Set this greater than 2500 and solve for t:
100 * (1.5)^t > 2500
(1.5)^t > 25

Take the log of both sides and change the bases.
t > log(25) / log(1.5)
t > 7.939

Since the question asked about whole minutes, t = 8

0 minutes = $100
1 minute = $150 (100 x 1.50)
2 minutes = $225 (150 x 1.50)
3 minutes = $337.50 (225 x 1.50)
4 minutes = $506.25 (337.5 x 1.50)
5 minutes = $759.38 (etc.)
6 minutes = $1,139.07
7 minutes = $1,708.61
8 minutes = $2,562.92

The bid will exceed $2,500 after 8 minutes

PROBLEM 2:

3 choices for the first letter
2 choices for the second letter
1 choice for the last letter

3 x 2 x 1 = 6 passwords

SLF
SFL
LSF
LFS
FLS
FSL

P.S. Not a very secure way to pick a password. :)

PROBLEM 3:

8 ways

QDD = 1 quarter, 2 dimes
QDNN = 1 quarter, 1 dime, 2 nickels
QNNNN = 1 quarter, 4 nickels
DDDDN = 4 dimes, 1 nickel
DDDNNN = 3 dimes, 3 nickels
DDNNNNN = 2 dimes, 5 nickels
DNNNNNNN = 1 dime, 7 nickels
NNNNNNNNN = 9 nickels

Answer 2

You can tackle these by brute force if you like. It might be tedious but it'll work.

Get out a calculator and write down the numbers you get by starting with $100 and multiplying over and over by 1.5 until you hit $2500.

Start with a new letter in the first position after listing all the different possible combinations of the other two after it --
SLF
SFL

LSF
LFS

FSL
FLS

For the last one make a similar list.

Answer 3

1. 2500 = 100(1.5)^n
25 = 1.5^n
n = log 25 / log 1.5 = 7.9387...

2. 6

3. If you need all of them, there is only 1 way to do it. (1 quarter, 1 dime, 2 nickels) If you can use only 2 of them, there are many more...