Question

Damon is building an enclosure for his pet dog. The enclosure is 10 feet wide and x
feet long. The cost per square foot of building the enclosure, c
, is a function of its length, as shown in the table below.

x c(x)
10 $8.00
12 $7.33
15 $6.67
20 $6.00
25 $5.60
Which statement best describes the average rate of change in c[x]
on the interval from x=10 to x=20? A.
The cost per square foot decreases by 10 cents on average for each extra foot of length.

B.
The cost per square foot is 10 cents less for a 20-foot-long enclosure than a 10-foot-long enclosure.

C.
The cost per square foot decreases by 20 cents on average for each extra foot of length.

D.
The cost per square foot is 20 cents less for a 20-foot-long enclosure than a 10-foot-long enclosure.

Answer 1

Average rate = (c(20) − c(10)) / (20 − 10) = (6.00 − 8.00)/10 = −0.20 dollars/ft = −20 cents/ft.

So C is correct: the cost per square foot decreases by 20 cents on average for each extra foot.