65
Math 150-06: Quiz #1 (Chapter 1)
Name:
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 because the number of widgets must be a whole number,
so the input is restricted to 2 decimal places
2. Consider the function V x   0.085 x  4.5 which gives the value of a certain antique (in $thousands).
Find and interpret V(4). (6 points)
V(4) = 0.085(4) + 4.5 = $4.84 thousand
This cannot be interpreted because we are not given the meaning
of the input variable.
3. Suppose that a certain home cost $125000 in the year 2000, but if sold this year (2007) it would cost
$153000.
(a) Assuming a linear relationship, find a model for the cost of the home x years after 2000.
C(x) = 4000x + 125000 dollars x years after 2000
(b) Give the slope of your model (including units).
m = $4000 per year
(3 points)
(6)
4. The amount of motor vehicle taxes collected (in $millions) by a certain county in various years is
shown in the table below. (5 points each)
Year
1992
1994
1996
1998
2000
Amount
Collected
108
122
137
155
169
(a) Calculate the first differences for this data. Is the data “perfectly linear”?
14, 15, 18, 14 – so not “perfectly linear”
(b) Let x = the number of years since 1990 and find a linear regression model for the data.
A1(x) = 7.75x + 91.7 million dollars
(c) Let x = the number of years since 1992 and find a linear regression model for the data.
A2(x) = 7.75x + 107.2 million dollars
(d) Let x = the number of years since 1900 and find a linear regression model for the data.
A3(x) = 7.75x – 605.8 million dollars
(e) What is the slope of each of your models (including units)?
M = $7.75 million per year
(f) Using each of your models, predict the amount in taxes that was collected in 2004.
A1(14) = A2(12) = A3(104) = #200.2 million