Question

the consumer price index compares the cost of goods and services over various years, where 1967 is used as t=0. The same goods that cost $100 in 1967 cost $184.50 in 1977. Find an exponential function to model this data. Estimate what those goods would cost in 2005

Answer 1

• f(t) = 100·1.845^(t/10)
• $1025.15

Explanation:

(a) The given numbers can be put directly into the form ...

... f(t) = (initial value) · (ratio)^(t/(time to achieve that ratio))

Here, we have an intial value of $100, and a ratio of $184.50/$100 = 1.845. The time to achieve that multiplication is 10 years (1967 to 1977). So, the equation can be written ...

... f(t) = 100·1.845^(t/10)

(b) You want to find f(38).

... f(38) = 100·1.845^(38/10) = 100·1.845^3.8 ≈ 1025.15 . . . dollars