Math 94
Practice Final
No notes or phones are allowed. Please show all your work on this paper. Simply each answer fully.
Good luck! Each problem is worth 2 points unless otherwise specified. Partial points may be used for
scoring. Deduction for work done in pen or for work that is hard to follow:_______ (up to 2 points)
1) Write as a single logarithm:
2) Solve the system:
2a  6b  4
3a  b  6
3) Given f ( x)  x 2  2 x , find f (a  3) .
4) Simplify
5) Solve
3
x2 y 4  3 x2 y6
6) Write the equation of a circle with a center of (9,-3) and a radius of 16.
7) Write in the form a  bi :
3i
2i
8) Solve
9) Solve
. Round to 4 decimal places, if necessary.
10) Solve
Round to 4 decimal places, if necessary.
11) You invest $2,000 at 4.5% interest, compounded continuously. What is the value of your
investment after 5 years? Round to the nearest dollar. Use the formula
.
12) A population of a certain country has an exponential growth rate of 2.5% per year. If that growth
rate is maintained, how long until the population doubles? Round to the nearest year. Use
.
13) Plot several points and graph
14) Plot several points and graph
15) Solve
16) In 1999, there were 5.978 billion people in the world. In 2012, there were 7.052 billion
people in the world.1 Formulate a linear function to model the number of people,
, in
billions, t years after 1999. Round the slope to 3 decimal places.
17) Solve for q:
18) Rewrite using radical notation and then simplify:
1
Source: https://en.wikipedia.org/wiki/World_population
19) [Set up only!] Cool Cat Coffee sells 8-oz cups of coffee for $1.75, 12-oz cups of coffee
for $2.30, and 16-oz cups of coffee for $2.65. During a certain period, they sold 80 cups
of coffee for a total of $181.35. The total amount of coffee sold was 980 oz. You want
to find how many cups of each type they sold.
i) Clearly label 3 variables.
ii) Set up 3 equations involving the variables you labeled in (i).
20) Graph
21) In the following right triangle
and
. Find the length of the missing side.
Give the exact value or a decimal approximation rounded to 2 decimal places.
c
a
b
22) Simplify
23) Rewrite the following sum using sigma notation.
24) Given
, find
.
25) Graph
26) Find the domain of
. Write your answer in interval notation.