100
Math 150 – 09: Test #1 (Chapters 1-2)
Name:
Show as much work as possible to receive full credit. Correct answers with no work may not receive full
credit.
1. Consider the function Cn = the cost (in $thousand) when a company produces n hundred widgets
each month.
(a) What are the input and output of this function? What are the input and output variables?
Whatare the input and output units? (9 points)
input = # of widgets made each month
input var. = n
input units = hundred widgets
(b) Interpret (translate) the statement C7.41.68 .
output = cost
output var. = C
output units = $thousand
(3 points)
When the company produces 740 widgets each month, it will cost
them $1680.

(c) Write the statement “When the company produces 475 widgets each month, the cost is $985”
using function notation. (3 points)
C(4.75) = 0.985
(d) If a continuous model was found for this relation, would it be interpreted discretely or used
without restriction? Explain. (5 points)
discretely interpreted because the number of widgets must be a
whole number, so the input is restricted to 2 decimal places
2. Describe each of the following function’s growth. Do not simply draw a picture; rather give the
“definition” of the growth. (4 points each)
(a) Linear growth
growth by a constant average rate of change (slope)
(b) Exponential growth
growth by a constant percent change
(c) Logistic growth
exponential growth that levels off
3. Describe the concavity of the graph for each of the following model type.
(3 points each)
(a) Exponential
always concave up
(b) Logarithmic
when increasing – concave down; when decreasing – concave up
(c) Logistic
is concave up then concave down when increasing and is concave
down and then concave up when decreasing
4. For each of the following discrete functions, find the most appropriate model, determine whether the
model should be discretely interpreted or interpreted without restriction, and then find the indicated
value. (9 points each)
(a) The amount of chlorofluorocarbons (CFC’s) released into the atmosphere (in millions of
kilograms) in various years is shown in the table. Estimate the amount released in 1985.
Year
1982
1984
1986
1988
CFC’s
337.4
359.4
376.5
392.8
C(x) = 9.165x + 320.7 million kg x years after 1980
Discretely interpreted because input is years
1985 = C(5) = 366.525 million kg
(b) The average length (in centimeters) of a girl x months old is shown in the table. Estimate the
average length of a girl that is 30 months old.
x
4
10
18
27
35
42
Length
61
74
83
89
93
95
L(x) = 40.574 + 14.652(ln(x)) cm at x months
Can be used without restriction
30 months = L(30) = 90.41cm
(c) The reaction activity (measured in Units per 100 microliters = U/100µL) is measured during
the first 18 minutes after the mixture in an experiment reached 95°C. Estimate the reaction
activity at 12.5 minutes.
Minutes
0
2
4
6
8
10
12
14
16
18
Activity
0.1
0.1
0.25
0.6
1
1.4
1.55
1.75
1.9
1.95
A(x) = 1.937/(1+29.06e-0.4211x) U/100µL after x minutes
Can be used without restriction
A(12.5) = 1.68 U/100µL
5. For each scatter plot shown below, state all models that should be considered as potential “best fits”
for the model. (3 points each)
(a)
(b)
Exponential
Quadratic
Quadratic
(c)
(d)
Linear
Logistic
(e)
Logarithmic
Quadratic
(f)
Cubic
6. For each of the following collections of data, find the most appropriate model, and estimate the
indicated value. (7 points each)
(a) The table below gives the monthly profit (in $million) made when a certain airline charges
$x for a round trip flight from Denver to Chicago. Estimate the profit when the airline
charges $240 and $315 for this flight.
x
200
250
300
350
400
450
Profit
3.08
3.52
3.76
3.82
3.70
3.38
P(x) = -0.000037x2 + 0.026x - 0.527 million dollars when charging $x
P(240) = $3.44 million
P(315) = $3.8 million
(b) The cumulative total number of tickets for an Alaskan cruise sold by the end of the xth week
is shown in the table below. Estimate the number of tickets sold during the 15th week.
x
Tickets
1
71
T ( x) 
4
197
tickets by the end of the xth week
7
524
10
1253
13
2443
16
3660
19
4432
22
4785
25
4923

5000.08
1 98.97e0.35x
T(15) – T(14) = 3290 – 2878 = 412 tickets