Since v 250000 when t 0 and v 10000 when t 10 the

Since V  250,000 when t  0 and V  10,000 when
t  10, the line passes through the points  0  250000  and

10  10000

. The slope of the line through these points is
given by m 
10,000  250,000
10  0
 
240,000
10
  24,000.
Using the point-slope form of an equation of a line with the
b.
c. In 2014, t  4 and V   24,000  4   250,000  154,000, or $154,000.
d. The rate of depreciation is given by  m , or $24,000  yr.
0
50,000
100,000
150,000
200,000
250,000
2 4 6 8 10 12
t
V
(10, 10000)
point  10  10000  , we have V  10,000   24,000  t  10  , or V   24,000 t  250,000.
23. Let the value of the workcenter system after t years be V . When t  0, V  60,000 and when t  4, V  12,000.
c.
0
10,000
20,000
30,000
40,000
50,000
60,000
1 2 3 4 5 6
t
V
24. The slope of the line passing through the points  0  C  and  N  S  is m 
S  C
N  0

S  C
N
 
C  S
N
. Using the
point-slope form of an equation of a line with the point  0  C  , we have V  C  
C  S
N
t , or V  C 
C  S
N
t .
25. The formula given in Exercise 24 is V  C 
C  S
N
t . When C  1,000,000, N  50, and
S  0, we have V  1,000,000 
1,000,000  0
50
t , or V  1,000,000  20,000 t . In 2013, t  5 and
V  1,000,000  20,000  5   900,000, or $900,000. In 2018, t  10 and V  1,000,000  20,000  10   800,000,
or $800,000.
26. The formula given in Exercise 24 is V  C 
C  S
N
t . When C  24,000, N  5, and S  0, we have
V  24,000 
24,000  0
5
t  24,000  4800 t . When t  3, V  24,000  4800  3   9600, or $9600.
27. a. D  S  
Sa
1  7
. If we think of D as having the form D  S   mS  b , then m 
a
1  7
, b  0, and D is a linear
function of S .
b. D  0  4  
500  0  4 
1  7
 117  647, or approximately 117  65 mg.
28. a. D  t  
 t  1 
24
a 
a
24
t 
a
24
. If we think of D as having the form D  t   mt  b , then m 
a
24
, b 
a
24
, and
D is a linear function of t .
b. If a  500 and t  4, D

4


4  1
24

500

 104  167, or approximately 104  2 mg.
Full file at

22
1
STRAIGHT LINES AND LINEAR FUNCTIONS
29. a. The graph of f passes through the points P
1
 0  17  5  and P
2
 10  10  3  . Its slope is
10  3  17  5
10  0
  0  72.
An equation of the line is y  17  5   0  72  t  0  or y   0  72 t  17  5, so the linear function is
f  t    0  72 t  17  5.
b. The percentage of high school students who drink and drive at the beginning of 2014 is projected to be
f  13    0  72  13   17  5  8  14, or 8  14%.