Question

The consumer price index compares the costs, c, of goods and services over various years. The same goods and services which cost $100 in 1983 cost $243 in 2017. Assume that the consumer price index follows a continuous exponential model (F = Pe^it).

      a. Find the function that estimates the consumer price index, c, t years after 1983. Round the growth rate to six decimal places.

      b. Use your answer from part a to estimate the year in which the consumer price index was $200.

      c. Use your answer from part a to estimate how much the goods and services which cost $100 in 1983 will cost in 2023.

      d. Find dc/dt.

      e. Use your answer from part d to estimate what the rate of change in the cost of the goods and services which cost $100 in 1983 will be in 2023.

Answer 1