1. ## Help

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.

2. Originally Posted by norwoodjay
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.