Complete this test without the use of a Calculator. For some problems, showing your work on a whiteboard will be enough. Others will prompt you for a numeric answer, which might be a number, an expression or an equation. These prompts will contain a little keyboard icon that will give you all the formatting tools you'll need to enter such an answer. Within this formatting tool, typing a forward slash (/) will make a division bar!
Below is a graphic with the Laws of Logs, numbered 1, 2 or 3. Use these numbers later in the test when prompted.
Also below is a picture that gives you the functions of the editing icons you will find in any "show your work" whiteboard. NOTE: It will probably be faster to use the built-in editing tools, but if you are having any problems, you can always upload a photo of the problem's work completed on paper to any "show your work" whiteboard.
8 points
8
Question 1
1.
Given the function:
Sketch a quick graph in "show your work" and then give the Domain, Range and equation for the asymptote for that function, as prompted on the "show your work" page.
8 points
8
Question 2
2.
Given the function:
Sketch a quick graph in "show your work" and then give the Domain, Range and equation for the asymptote for that function, as prompted on the "show your work" page.
8 points
8
Question 3
3.
Given the function:
Sketch a quick graph in "show your work" and then give the end behavior, as prompted on the "show your work" page.
4 points
4
Question 4
4.
Simplify the expression:
4 points
4
Question 5
5.
What two consecutive integers (integers right next to each other) does log(101) fall between? You will write two answers that fill in the blanks in this statement: ______ < log(101) < ______. Justify your answers for full credit - just putting numbers in the spaces will not receive full credit.
7 points
7
Question 6
6.
Solve for x, leaving exact answers in simplified form. If multiple answers, separate them with a comma, then a space.
Show your work.
7 points
7
Question 7
7.
Solve for x, leaving exact answers in simplified form. If multiple answers, separate them with a comma, then a space.
Show your work.
7 points
7
Question 8
8.
Solve for x, leaving exact answers in simplified form. If multiple answers, separate them with a comma, then a space.
Show your work.
8 points
8
Question 9
9.
Expand the Expression as far as you can, showing ONLY ONE change per line. For each step you show, IF it involves a law of logs, you must cite the Law number next to that line. [Laws 1, 2 and 3 are at the beginning of the test, and are numbered so you can easily refer to them in this problem.]
8 points
8
Question 10
10.
Condense the Expression into a single logarithm, showing ONLY ONE change per line. For each step you show, IF it involves a law of logs, you must cite the Law number next to that line. [Laws 1, 2 and 3 are given at the beginning of the test, and are numbered so you can easily refer to them in this problem.]
3 points
3
Question 11
11.
Simplify as much as possible.
The answer will be a number or a fraction.
3 points
3
Question 12
12.
Simplify as much as possible.
The answer will be a number or a fraction.
3 points
3
Question 13
13.
Simplify as much as possible.
The answer will be a number or a fraction.
5 points
5
Question 14
14.
The half-life is the time it takes for somesubstance to decay to half of its initial amount. The radioactive decay equation is modeled by the following formula:
N(t) is the quantity of substance after time t (in seconds).
No is the initial quantity of the substance.
L is the decay constant, which depends on your substance. (NOT the same as the half-life of the substance.)
The half-life of a certain substance is 30 years. Find the decay constant L for this substance.
7 points
7
Question 15
15.
The amount in milligrams of a drug in the body t hours after taking a pill is given by the following formula:
When will the patient have 10% of the initial dosage left in their body?
0 points
0
Question 16
16.
[BONUS] Albert deposited x dollars into a new account that earned 6.5% annual interest, compounded annually. One year later, Albert deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of those two years, find an expression for x in terms of w, x(w).
