### MATH 100 Quiz 6

**Name:**

You may use a calculator on this quiz. You may not use a cell phone or
computer. To receive full credit please show your work carefully and
give justifications for your answers. If you find that you are
spending a lot of time on one problem, leave it blank and move on to
the next. There are questions on both sides of this paper.

- (3.1#6) Suppose you have $1000 and plan to invest it at an interest rate of 4% for 5 years.

a) (5 pts) What will your account balance be after 5 years if the interest is compounded anually? (A = P(1+r)^{t}.)

b) (5 pts) What will your account balance be after 5 years if the interest is compounded continuously? (A = Pe^{rt}.)

- (3.1#7) On the grids provided below, sketch the graphs of:

a) (10 pts) f(x) = 3^{x}

b) (10 pts) g(x) = log_{3}x

- (3.2#1: 15 pts) Give the equivalent exponential form of the equation 2 = log
_{4}16

- (3.2#4: 15 pts) Evaluate log
_{ 9}81.

- (3.3#2,5) Expand the expressions below and simplify them as far as is possible without use of a calculator.

a) (10 pts) log_{7}( ^{7}/_{y})

b) (15 pts) log_{b}(y^{7}z)

- (3.3#9: 15 pts) Condense the expression into a single logarithm whose coefficient is 1:

3ln(x+9) - ln(x).

**Bonus** (5 points) Use the change of base formula to describe how you could graph
f(x) = log_{8}(x) on your calculator.