Pre-Calculus Logarithmic and Exponential Explorer______________________________

Chapter 3 Test Review

1. Graph both functions below on the same axis by listing the asymptotes, at least two points for each, as

well as the domain and range.

43 2+=

−xy 2)4(log3 +−= xy

Asymptote:_______________ Asymptote:__x = 4_________

Points:__________________ Points:___________________

Domain:_________________ Domain:_________________

Range:___________________ Range:___________________

2. Algebraically, find the inverse of the function 43 2+=

−xy . How does this relate to your equations,

asymptotes, domain and range, and graphs found in #1?

3. You have chosen to invest $7,500 at 7.5% interest compounded quarterly. a) How much money will you have after 10 years? b) How long would it take to reach the same balance if the money was invested in an account that continuously compounds the interest at 4%? a) Balance Comp. Quarterly__________________ b) Time Comp. Continuously__________________

4. Write in exponential form: 5. Write in logarithmic form: 6. Evaluate to 3 decimal places:

log7(2401) = 4 1664 3/2= 81log4

7. Expand and simplify, if possible:

a. ( )34

4 48log yx b.

46

72

1log

d c.

+

rq

p 1ln

34

4

44 loglog48log yx ++

yx 4444 log3

1log416log3log +++

yx 444 log3

1log423log +++

8. Simplify each of the following into a single logarithm:

a. cba log2

1log3log2 +− b. x2log

3

11− c.

−− zyx ln3ln

8

1ln2 5

9. Solve each of the following equations. Round your answer to 3 decimal places if necessary.

a. 41log 2 =−x b. 4975 12=

+x c. 54ln2 =−x

10. Solve each of the following equations. Round your answer to 3 decimal places if necessary.

a. ( ) 28loglog 33 =−+ xx b. 526)2(3 4=−

−x

c. ln(x + 1) – ln(x – 2) = ln(2) d.

x

x

5

62

9

127

=

+−

e. 0523 2=−+

xxee f. 5

98

10254

=+

x

13. Carbon-14 is commonly used in dating objects because it has a large half-life. A half-life is the amount of time it takes for half (aka 50%) of an element to decay). The equation representing the decay is given by where N is the final amount, N0 is the initial amount, k is the growth/decay constant, and t is measured in years. a. Suppose you have a sample which takes approximately 1343 years for 15% of the sample to decay, find the value of the constant k to 5 decimal places. b. What is the half-life (in years) of Carbon-14? (How long for half a sample to decay?)

14. In a typing class, the average number of words typed per minute, N, after t weeks was found to be

teN

12.04.51

157−

+=

a. How many words per minute should a student be able to type if they have been in the class for 5

weeks?

b. Find the time necessary to type 75 words per minute?

0

ktN N e=