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 + 7 x − x 2 20 , 000 ; x = 10 , 000
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 + 7 x − x 2 20 , 000 ; x = 10 , 000
Solution Summary: The author calculates the average rate of change for the function C(x)=20,000+7x-
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
+
7
x
−
x
2
20
,
000
;
x
=
10
,
000
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.
World Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011).
†A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below.
1: 1,800 billion dollars
2: 1,775 billion dollars
3: 1,750 billion dollars
4: 1,730 billion dollars
5: 1,760 billion dollars
6: 1,760 billion dollars
7: 1,850 billion dollars
8: 1,900 billion dollars
9: 1,950 billion dollars
10: 1,980 billion dollars
(a)
If you want to model the expenditure figures with a function of the form
f(t) = at2 + bt + c,
would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.]
We would expect the coefficient to be positive because the curve is concave up.
We would expect the coefficient to be negative because the…
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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