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 160 in 2010. (Enter exact numerical values. Do not round.) C(t) = 0.009 - 0.096 + 3 + 4.85t + 58.2 X (b) What does the model from part (a) predict for the consumer costs in 2020? (Round your answer to the nearest cent.) $ 367.4
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 160 in 2010. (Enter exact numerical values. Do not round.) C(t) = 0.009 - 0.096 + 3 + 4.85t + 58.2 X (b) What does the model from part (a) predict for the consumer costs in 2020? (Round your answer to the nearest cent.) $ 367.4
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 16TI: Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds....
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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 160 in 2010. (Enter exact numerical values. Do not round.)
C(t) =| 0.009
0.096 +
3
+ 4.85t + 58.2 X
(b) What does the model from part (a) predict for the consumer costs in 2020? (Round your answer to the nearest cent.)
$ 367.4
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