A sports trainer has monthly costs of $69.95 for phone service and $39.99 for his website and advertising. In addition he pays a $20 fee to the gym for each session in which he trains a client. ( See Example 11 ) a. Write a cost function to represent the cost C ( x ) for x training sessions for a given month. b . Write a function representing the average cost C ¯ ( x ) for x sessions. c . Evaluate C ¯ ( 5 ) , C ¯ ( 30 ) , and C ¯ ( 120 ) . d . The trainer can realistically have 120 sessions per month. However, if the number of sessions were unlimited, what value would the average cost approach? What does this mean in the context of the problem?
A sports trainer has monthly costs of $69.95 for phone service and $39.99 for his website and advertising. In addition he pays a $20 fee to the gym for each session in which he trains a client. ( See Example 11 ) a. Write a cost function to represent the cost C ( x ) for x training sessions for a given month. b . Write a function representing the average cost C ¯ ( x ) for x sessions. c . Evaluate C ¯ ( 5 ) , C ¯ ( 30 ) , and C ¯ ( 120 ) . d . The trainer can realistically have 120 sessions per month. However, if the number of sessions were unlimited, what value would the average cost approach? What does this mean in the context of the problem?
Solution Summary: The author explains how the cost function can be represented as C(x)=mx+b, where m is the variable cost to produce an item, and b the fixed cost.
A sports trainer has monthly costs of $69.95 for phone service and $39.99 for his website and advertising. In addition he pays a $20 fee to the gym for each session in which he trains a client. (See Example 11 )
a. Write a cost function to represent the cost
C
(
x
)
for x training sessions for a given month.
b. Write a function representing the average cost
C
¯
(
x
)
for x sessions.
c. Evaluate
C
¯
(
5
)
,
C
¯
(
30
)
,
and
C
¯
(
120
)
.
d. The trainer can realistically have 120 sessions per month. However, if the number of sessions were unlimited, what value would the average cost approach? What does this mean in the context of the problem?
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