Question

Suppose the cost of producing tires, t, is defined by C(t) = -0.45+2 + 12+ 450. Determine

which of the following intervals has the greatest average rate of change for the cost to
produce tires.
A
Between 2 and 4 tires
B
Between 46 and 48 tires
C
Between 12 and 14 tires
D
Between 22 and 24 tires

Answer 1

Average rate of change is greatest in the interval (46. 48)

Explanation:

Average rate of change in the interval (2, 4)

= 9.3

Average rate of change in the interval (46, 48)

= -30.3

Average rate of change in the interval (12, 14)

= 0.3

Average rate of change in the interval (22, 24)

= --8.7

I did the algebra CFU and I got it correct so trust me ;)

Answer 2

Option (A)

Explanation:

Function to represent the cost of producing 't' tires is,

C(t) = -0.45t² + 12t + 450

Since average rate of change of the function in the interval (a, b) is given by,

Average rate of change =
`(f(b)-f(a))/(b-a)`

Following this rule,

Average rate of change in the interval (2, 4)

=
`(C(4)-C(2))/(4-2)`

=
`(490.8-472.2)/(4-2)`

= 9.3

Average rate of change in the interval (46, 48)

=
`(-10.8-49.8)/(2)`

= -30.3

Average rate of change in the interval (12, 14)

=
`(529.8-529.2)/(2)`

= 0.3

Average rate of change in the interval (22, 24)

=
`(478.8-496.2)/(24-22)`

= --8.7

Average rate of change is greatest in the interval (2, 4)

Option (A) will be the answer.