C O | wwww.webassign price index (CPI) how prices have with 1995 as a of 100, a
ID: 2890255 • Letter: C
Question
C O | wwww.webassign price index (CPI) how prices have with 1995 as a of 100, a year with CPI 150 that 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-0.009t? -0.06+4.85 dt dollars per year, where t O represents 1990. (a) Find the function thet models Cte), if the CPI was 155 in 2010. (Enter exact numerical values. Do not round.) cle) 155 (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? The model predicts lower consumer costs in 2030 * The model predicts equal consumer costs in 2010 and 2030. The model predicts higher consumer costs in 2030. 0Explanation / Answer
dC/dt=0.009t2-0.096t+4.85
Integrating both sides
C(t)= 0.003t3-0.048t2+4.85t+c
2015 means t=2015-1990=25
155=0.003(25)3-0.048(25)2+4.85(25)+c
c=16.875
C(t)= 0.003t3-0.048t2+4.85t+16.875
b. 2030 means t=2030-1990=40
C(40)=0.003(40)3-0.048(40)2+4.85(40)+16.875=326.08
c. Correct option is the last option
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