MATH 121     Extra Problems for Test 6

This is an old test and quiz that I gave. As always make sure you understand all concepts covered in homework, quizzes, handouts, and textbook problems.

1.) Solve the following equations for x:

(a.)

(b.)

(c.)

(d.)

(e.) log(x⁴) = (log x)³

(f.) 4(3^x) + 5(3^-x) = 9

2.) Evaluate the following expressions. (Assume b > 1)

(a.)	(b.)
(c.)	(d.)
(e.) (Give your answer accurate to the hundredths place.)	(f.)

3.) Write as a single logarithm in simplest form. (Assume x, y > 0.)

4.) Suppose log _b2 = 0.3869 & log _b3 = 0.6131 . Evaluate log _b(9/2) .

5.) If you just received a large sum of money and you want to buy a $100,000 house in 5 years, how much should you invest at 5% annual interest compounded daily in order to pay cash for the house.

6.) Suppose the quantity Q (in grams) of a radioactive substance present at a time t (in days) is given by .

(a.) Find the initial quantity of the substance. (Initial quantity means quantity at time zero.)
(b.) Find the quantity left after 20 days.

7.) Solve for x.

8.) Simplify the following expression completely:

9.) For each of the following write down the formula that you use as well as your answer. Round your answer to the nearest penny. If you put $500 into a savings account that pays 6% annual interest, how much will you have after 2 years if it is compounded :

quarterly?
monthly?
daily?
continuously?

10.) A certain kind of glass that is 3 millimeters thick filters out 35% of the light that goes through it.

1. How much light would filter through a piece of the same kind of glass, if it is 6mm thick?
2. How much light would filter through a piece of the same kind of glass, if it is 5mm thick?
3. How thick would the glass need to be in order for 70% of the light to be filtered out?

11.) Match the graphs to each of the following equations. (Each graph is used only once.)

(i.) f(x) = 2^x _____                    (ii.) f(x) = log₂x ____

(iii.) f(x) = (½)^x ___             (iv.) f(x) = - log₂x ____

(v.) f(x) = 2(2)^x ____           (vi.) f(x) = log₂(-x) ____

Answers:
1.) a.) x = 6/5         b.)            c.)         d.) no solution since you get which is less than zero.                     e.) x = 1, 100, or 0.01                     f.) x = 0 or
2.) a.) -3            b.) 0                 c.) 3            d.) no solution.             e.) 1.26              f.) -1
3.)
4.) 2(0.6131) - 0.3869 = 0.8393
5.) $77,881.41
6.) a.) 500 grams b.) 183.94 grams
7.) x = -3/2 or x = 1
8.)
9.) $563.25, $563.57, $563.74, $563.75 respectively
10.) (a.) 42.25% (b.) 48.77% (c.) 8.38 mm
11.) (i.) d (ii.) a (iii.) f (iv.) e (v.) c (vi.) b