Question

1. 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. ____________   

2. Fruit flies are placed in a half-pint milk bottle with a banana (for food) and yeast plants (for food and to provide a stimulus to lay eggs).  Suppose that the fruit fly population after t days is modeled by

              230

F = ------------------.   

        1 + 56.5e^-0.37t

      a. Determine the initial population of fruit flies.   ____________  

      b. After how many days will the fruit fly population reach 100?   ____________  

      c. What is the maximum number of fruit flies supportable in this situation?   ____________

      d. Find dF/dt. ____________  

      e. Use your answer from part d to estimate what the rate of change in the number of fruit flies after 10 days. ____________   

Answer 1