Math 124 Exam 1 Sept. 14, 2006
Name
Directions
1.
SHOW YOUR WORK and be thorough in your solutions.
Partial credit will only be given for work
shown.
2. Any numerical answers should be left in exact form, i.e, no decimal approximations.
3. You may use calculators.
Good luck!
1.
One of the following tables of data is linear and one is exponential.
Say which is which and give an
equation that best fits each table.
Solution:
A linear function will have constant
differences
in
y
with constant changes in
x
. An exponential function will
have constant
ratios
in
y
with constant changes in
x
. Notice that in the first table the ratios of
y
values is
constant approx. 0
.
84. We use
y
=
Ca
x
. Since
y
= 3
.
12 when
x
= 0, we see that
C
= 3
.
12. Using the point
(1
.
00
,
2
.
20), we see that 2
.
2 = (3
.
12)
a
1
, hence
a
=
2
.
2
3
.
12
. This gives
y
= 3
.
12
2
.
2
3
.
12
x
The second table,
being linear, has a slope of
m
=
3
.
94

2
.
71
0
.
5
= 2
.
46. Using
y

y
1
=
m
(
x

x
1
), we have
y

2
.
71 = 2
.
46(
x

0),
or
y
= 2
.
46
x
+ 2
.
71
.
2. From the graph of
y
=
f
(
t
) below, describe the domain and range of
f
(
t
). In a sentence, apply the general
definition of “function” to explain why you think that the given curve is in fact a function.
Solution:
The domain is simply the input values for the function, roughly
[1989
,
1992]
The range is the possible
output vales of the function, roughly
[2800
,
4100]
The curve is a function since every input value has
at
most
one output.
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 Spring '08
 KENNEDY
 Calculus, Approximation, Derivative, lim, 10 feet, 18 feet, 26 feet

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