Question

The value of a mountain bike in dollars,
y
, can be modeled by the constraint
y
=
500
(
0.80
)
x
where
x
is the number of years after purchase.



Which statement is TRUE about the possible data point?



A.
The data point
(
4
,
204.8
)
represents the value of the mountain bike after
4
years, which is
$
204.80
.

This value is a constraint because the value of the mountain bike is decreasing each year.

B.
The data point
(
4
,
204.8
)
represents the value of the mountain bike after
4
years, which is
$
204.80
.

This value is not a constraint because the value of the mountain bike is increasing each year.

C.
The data point
(
−
1
,
625
)
represents the value of the mountain bike
1
year before purchasing, which is
$
625.00
.

This value is a constraint because the value of the mountain bike is decreasing each year.

D.
The data point
(
−
1
,
625
)
represents the value of the mountain bike
1
year before purchasing, which is
$
625.00
.

This value is not a constraint because the value of the mountain bike is increasing each year.

Answer 1

A.

Check: y = 500(0.80)^4 = 500(0.4096) = 204.8, so (4, 204.8) corresponds to $204.80 after 4 years. Since 0.80 < 1 the bike’s value decreases each year, and x is years after purchase (x ≥ 0), so this point is a valid one for the model.