Dimensional Analysis and Exponential Models Module
(approximately 1.5 weeks)
Topics and Objectives
1. Dimensional Analysis (1 hr)
a. Convert from one unit to another unit.
2. Exponential Functions and Their Inverses (1 hr)
a. Evaluate a function at a given value.
b. Match an exponential function to its graph.
3. Exponential Growth and Decay (1.5 hr)
a. Solve applications problems involving exponential growth and decay.
Possible Test Questions
CEGM1-a
TM1. There are 7 dweebs in a twerp and 4 twerps in a geek.
a) Convert 9 geeks to dweebs. Give exact answers.
b) Convert 192 cubic twerps to cubic geeks. Give exact answers.
TM2. There are 7 dweebs in a twerp and 4 twerps in a geek. There are 6 springs in a
river.
a) Convert 60 dweebs per spring to twerps per rivers. Give exact answers.
b) Convert 25 twerps per square river to dweebs per square spring. Give exact
answers.
CEGM 2-a
TM1. Use a calculator to estimate e0.12 with four decimal place accuracy.
A.
B.
C.
D.
E.
1.1275
-2.1203

1.3183
-0.9208
none of the choices above are correct
TM2. Use a calculator to estimate ln12 to four decimal place accuracy.
A. 1.0792
B. 162754.7914
C. 12.0000

D. 2.4849
E. none of the choices above are correct
TM3. The population of caribou in a particular wilderness area is given by the function
P(t )  326e0.032t where t is measured in years since 1970. What will the caribou
population be in 2010?

A.
B.
C.
D.
E.
13,050
1173
4
13,464
none of the choices above are correct
CEGM 2-b
TM1. Match the following functions with their graphs.
a. y  ae3t
b. y  ae1.75t
c. y  ae0.75t
I
II


A.
B.
C.
D.
E.
III

a-I; b-II; c-III
a-III; b-II; c-I
a-III; b-I; c-II
a-I; b-II; c-III
none of the choices above are correct
CEGM 3-a
TM1. A bacteria culture doubles every hour. Find the model and use it to estimate the
bacteria population in 5 hours 20 minutes if the culture initially contained 50
bacteria.
A.
B.
C.
D.
E.
17,523
1838
2016
15,136
none of the choices above are correct
TM2. The population of caribou in a particular wilderness area is given by the function
P(t )  326e0.032t where t is measured in years since 1970. What is the initial
population of caribou?
A. 1
B. 10

C. 326
D. 163
E. none of the choices above are correct
TM3. The population of caribou in a particular wilderness area is given by the function
P(t )  326e0.032t where t is measured in years since 1970. What will the caribou
population be in 2010?

A.
B.
C.
D.
E.
13,050
1173
4
13,464
none of the choices above are correct
TM4. The population of caribou in a particular wilderness area is given by the function
P(t )  326e0.032t where t is measured in years since 1970. What is the relative
growth rate of this caribou population?

A.
B.
C.
D.
E.
.032%
1.032%
3.4199%
3.2%
none of the choices above are correct
TM5. Technetium 99m is a radioactive substance introduced into the blood stream for
medical imaging. The half-life of Technetium 99m is 4 hours. If 30 cc are
administered, when will there be 5 cc in the blood? Use four decimal places for
computations and answers.
NOTE: The following provided problems:
Terri Miller (TM)