The Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices in 1982–84. We can find the inflation rate for a given time period by calculating the percent of change in the CPI over that time period. For example, the CPI in 2005 was 195.3 and in 2009 it was 214.5, so the inflation rate was 214.5 − 195.3 195.3 ≈ 0.098 = 9.8 % . Use the given graph to do Exercises 47–50. Your answers may vary slightly due to rounding. Effect of inflation on the cost of cars. a. Calculate the inflation rate from 1990 to 2010. b. If a car cost $17,000 in 2010, use the inflation rate from part (a) to estimate what the car would have cost in 1990.
The Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices in 1982–84. We can find the inflation rate for a given time period by calculating the percent of change in the CPI over that time period. For example, the CPI in 2005 was 195.3 and in 2009 it was 214.5, so the inflation rate was 214.5 − 195.3 195.3 ≈ 0.098 = 9.8 % . Use the given graph to do Exercises 47–50. Your answers may vary slightly due to rounding. Effect of inflation on the cost of cars. a. Calculate the inflation rate from 1990 to 2010. b. If a car cost $17,000 in 2010, use the inflation rate from part (a) to estimate what the car would have cost in 1990.
Solution Summary: The author calculates the inflation rate for a given time period by calculating the percent of change in CPI.
The Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices in 1982–84. We can find the inflation rate for a given time period by calculating the percent of change in the CPI over that time period. For example, the CPI in 2005 was 195.3 and in 2009 it was 214.5, so the inflation rate was
214.5
−
195.3
195.3
≈
0.098
=
9.8
%
. Use the given graph to do Exercises 47–50. Your answers may vary slightly due to rounding.
Effect of inflation on the cost of cars.
a. Calculate the inflation rate from 1990 to 2010.
b. If a car cost $17,000 in 2010, use the inflation rate from part (a) to estimate what the car would have cost in 1990.
A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
Chapter 8 Solutions
Mathematics All Around, Books a la carte edition (6th Edition)
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