The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a reference of 100, a year with CPI = 150 indicates that consumer costs in that year were 1.5 times the 1995 costs. With labor data from a country for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by dC 0.009t2 – 0.096t + 4.85 dt dollars per year, where t = 0 represents 1990. (a) Find the function that models C(t), if the CPI was 180 in 2010. (Enter exact numerical values. Do not round.) C(t) = %3D (b) What does the model from part (a) predict for the consumer costs in 2030? (Round your answer to the nearest cent.) $ How does this compare to 2010? C The model predicts higher consumer costs in 2030. The model predicts lower consumer costs in 2030. The model predicts equal consumer costs in 2010 and 2030.
The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a reference of 100, a year with CPI = 150 indicates that consumer costs in that year were 1.5 times the 1995 costs. With labor data from a country for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by dC 0.009t2 – 0.096t + 4.85 dt dollars per year, where t = 0 represents 1990. (a) Find the function that models C(t), if the CPI was 180 in 2010. (Enter exact numerical values. Do not round.) C(t) = %3D (b) What does the model from part (a) predict for the consumer costs in 2030? (Round your answer to the nearest cent.) $ How does this compare to 2010? C The model predicts higher consumer costs in 2030. The model predicts lower consumer costs in 2030. The model predicts equal consumer costs in 2010 and 2030.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 1TI: Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use...
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The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a reference of 100, a year with
CPI = 150
indicates that consumer costs in that year were 1.5 times the 1995 costs. With labor data from a country for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by
| dC |
| dt |
Transcribed Image Text:The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a reference of 100, a year with CPI = 150 indicates that consumer costs in that year were 1.5 times the 1995
costs. With labor data from a country for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by
dC
0.009t2 – 0.096t + 4.85
dt
dollars per year, where t = 0 represents 1990.
(a) Find the function that models C(t), if the CPI was 180 in 2010. (Enter exact numerical values. Do not round.)
C(t) =
%3D
(b) What does the model from part (a) predict for the consumer costs in 2030? (Round your answer to the nearest cent.)
$
How does this compare to 2010?
C The model predicts higher consumer costs in 2030.
The model predicts lower consumer costs in 2030.
The model predicts equal consumer costs in 2010 and 2030.
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