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= 0.009t^2-0.096t+4.85 dollars per year, where t=0 represents 1990. (a) Find the function that models C(t), if the CPI was 175 in 2010. (b) What does the model from part (a) predict for the consumer costsin 2040?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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= 0.009t^2-0.096t+4.85
dollars per year, where t=0 represents 1990.
(a) Find the function that models C(t), if the CPI was 175 in 2010.
(b) What does the model from part (a) predict for the consumer costsin 2040?
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