Question

The function
P
(
n
)
=
−
0.02
n
2
+
30
n
−
3
,
000
models the profit, in dollars, that Jeremy expects from selling
n
handcrafted aprons at his store.



Which statement BEST interprets the average rate of change of this function from
n
=
750
to
n
=
1
,
000
?



A.
Jeremy expects his profit to increase by $0.20 for each additional apron he sells between 750 and 1,000 aprons.

B.
Jeremy expects his profit to increase by $5.00 for each additional apron he sells between 750 and 1,000 aprons.

C.
Jeremy expects his profit to decrease by $0.20 for each additional apron he sells between 750 and 1,000 aprons.

D.
Jeremy expects his profit to decrease by $5.00 for each additional apron he sells between 750 and 1,000 aprons.

Answer 1

Average rate of change = (P(1000) − P(750)) / (1000 − 750).

P(1000) = −0.02(1000)^2 + 30(1000) − 3000 = 7000.
P(750) = −0.02(750)^2 + 30(750) − 3000 = 8250.

Average rate = (7000 − 8250) / 250 = −1250 / 250 = −5.

So Jeremy expects his profit to decrease by $5 for each additional apron sold between 750 and 1,000 aprons. Answer: D.