Review the following concepts if needed:

- Growth by Addition Help
- Growth by Multiplication Help
- Exponential Functions Help
- Rules for Exponentials Help
- Logarithms Help
- Rules for Logarithms Help
- Graphs Based on Logarithms Help

**Growth and Decay Practice Test**

A good score is eight correct. Answers are at the end of the article.

1 . Imagine a frog that jumps halfway to a wall. After 10 seconds, it jumps halfway to the wall again. After another 10 seconds, it jumps halfway to the wall once again. It keeps repeating this process. In theory, how long will it take to reach the wall after its first jump?

(a) More information is needed to answer this question.

(b) 10 ^{2} , or 100, seconds.

(c) 2 ^{10} , or 1024, seconds.

(d) It will never reach the wall.

2 . Imagine a frog that jumps halfway to a wall. After 4 seconds, it jumps halfway to the wall again. After 2 seconds, it jumps halfway to the wall again. After 1 second, it jumps halfway to the wall again. The frog keeps repeating this process, but the intervals between jumps keep getting half as long: ½ second, then ¼ second, and so on. In theory, how long will it take to reach the wall, if we start timing it the moment it finishes its first jump?

(a) More information is needed to answer this question.

(b) 8 seconds.

(c) 4 ^{2} , or 16, seconds.

(d) 2 ^{8} , or 256, seconds.

3 . Consider this sum of numbers:

*S* = 4 −4 + 4 −4 + 4 −4 + 4 −4 + . . .

Which of the following statements is true?

(a) *S* is a convergent series.

(b) *S* is an arithmetic series.

(c) *S* is an infinite series.

(d) *S* is not a series.

4 . What is the base–10 logarithm of 0.00001?

(a) *e* /10

(b) −e/10

(c) 5

(d) −5

5 . Which of the following points cannot, in theory, be shown on a log-log ( *x,y* ) coordinate system?

(a) The point corresponding to *x* = 1 and *y* = 1.

(b) The point corresponding to *x* = 0 and *y* = 1.

(c) The point corresponding to *x* = 10 and *y* = 10.

(d) The point corresponding to *x* = 0.1 and *y* = 0.1.

6 . What is the natural logarithm of *e?*

(a) 0

(b) 1

(c) *e*

(d) 1/ *e*

7 . Suppose a sequence of numbers is such that each value is exactly 4 less than the value before it. This is an example of

(a) a geometric progression

(b) an arithmetic progression

(c) a logarithmic progression

(d) a fractional progression

8 . Suppose you’re listening to a compact disc on your new high-powered stereo sound system. The VU (volume unit) meter needles are kicking up to the points marked 0 dB, exactly where the black lines end and the red lines begin. If you increase the gain so the needles are kicking up to + 6 dB in the red zone, the sound power coming from the speakers has approximately

(a) doubled

(b) quadrupled

(c) increased by a factor of 6

(d) increased by a factor of 2 ^{6} , or 64

9 . Suppose you take a 4-week temporary job with a 5-day work week. The boss promises that you’ll be paid daily in US dollars ($): $1.00 at the end of the first day, $2.00 at the end of the second day, and doubling each day after that for the entire period. What should this indicate to you?

(a) The boss is a liar or an unwise wealthy person.

(b) The payment is meager, and you should look for another job.

(c) Your accumulated pay, day by day, will represent a convergent series.

(d) Nothing, without more information.

10 . Suppose a sequence of numbers is such that each value is exactly 25% of the value before it. This is an example of

(a) a geometric progression

(b) an arithmetic progression

(c) a logarithmic progression

(d) a fractional progression

**Answers**

** **

**1 . d**

**
**

**2 . b**

3 . c

4 . d

5 . b

6 . b

7 . b

8 . b

9 . a

10 . a

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