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  1. #1
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    Consumer Price Index: The U.S. Consumer Price Index is approximated by

    A(t)=100e .024t

    where t represents the number of years after 1990. (For instance, since A(12) is about 133, the amount of goods that could be purchased for $100 in 1990 cost about $133 in 2002.) Use the function to determine the year in which costs were 25% higher than in 1990.
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  2. #2
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    Quote Originally Posted by norwoodjay View Post
    Consumer Price Index: The U.S. Consumer Price Index is approximated by

    A(t)=100e .024t

    where t represents the number of years after 1990. (For instance, since A(12) is about 133, the amount of goods that could be purchased for $100 in 1990 cost about $133 in 2002.) Use the function to determine the year in which costs were 25% higher than in 1990.
    Let us just follow what you were saying.

    in 1990, t = 0, A(0) = 100
    in 2002, t = 12, A(12) = 133
    And 133 is 33% higher than 100, so in 2002, costs were 33% higher than in 1990.

    In what year would the costs be 25% higher than in 1990?

    25% higher than 100 = 125, so,
    125 = 100e^(0.024t)
    e^(0.024t) = 125/100
    e^(0.024t) = 1.25
    Take ln of both sides,
    (0.024t)*ln(e) = ln(1.25)
    t = [ln(1.25)]/(0.024) = 9.29765, or say, 9 years.
    Therefore, in 1999, the costs are 25% higher than in 1990. ----answer.
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