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posledela
3 years ago
14

the consumer price index compares the cost of goods and services over various years, where 1967 is used as t=0. The same goods t

hat 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
Mathematics
1 answer:
Lisa [10]3 years ago
6 0

Answer:

  • f(t) = 100·1.845^(t/10)
  • $1025.15

Step-by-step 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

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You need to know r to find the number of hours Brandee worked. She got paid $800 for a presumed 40-hours of regular time, so made r = $20 per hour. The above formula will tell you she worked 48 hours in the pay period.

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