In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and h = 0 and 1 . Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] C ( x ) = 20 , 000 + 50 x + 10 , 000 x ; x = 100
In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and h = 0 and 1 . Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] C ( x ) = 20 , 000 + 50 x + 10 , 000 x ; x = 100
Solution Summary: The author calculates the average rate of change for the function C(x)=20,000+50x+10,000x
In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and
h
=
0
and 1. Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [HINT: See Example 1.]
The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012.
Year t (year since 2000)
0
6
12
Military Expenditure C(t)($ billion)
390
550
640
(a)
Compute the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement. HINT [See Example 1.]
Interpret the average rate of change.
This country's military expenditure increased at an average rate of about between 2006 and 2012.
(b)
Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. HINT [See Example 1.] (Round your answer to two decimal places.)
Interpret the average rate of change. (Round your answer to two decimal places.)
This country's military expenditure increased at an average rate of about between 2000 and 2012.
The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012.
Year t (year since 2000)
0
6
12
Military Expenditure C(t)($ billion)
380
540
660
(a)
Compute the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement.
Interpret the average rate of change.
This country's military expenditure increased at an average rate of about between 2006 and 2012.
(b)
Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. (Round your answer to two decimal places.)
Interpret the average rate of change.
This country's military expenditure increased at an average rate of about between 2000 and 2012.
In Exercises 7–12, describe the relationship between the two quantities.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.