Question

A gym charges a
$
100
fee to new members. They expect
1
,
000
new members. For each increase of
$
10
in the fee, there would be a reduction of
20
new members. The gym claims the function is
y
=
(
1
,
000
−
20
x
)
(
100
+
10
x
)
where
y
is the predicted revenue from memberships after
x
increases of
$
10
.



Which statement BEST explains the claim made about the function?



A.
The gym's function is incorrect because the signs of the terms are reversed.

B.
The gym's function is incorrect because the coefficients for the variable are reversed.

C.
The gym's function is correct because the
20
x
represents a reduction in members and
10
x
represents an increase in fees.

D.
The gym's function is correct because the
10
x
represents a reduction in members and
20
x
represents an increase in fees.

Answer 1

C. The function is correct because 1000 − 20x models the loss of 20 members per $10 increase and 100 + 10x models the $10 increase in fee per increase; their product gives revenue.