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The function helped Kira determine the rate at which electricity was being used for any day of the month. However, to manage total electrical production, Kira needs to determine a function that will accumulate the energy used over the course of the month. That is, she needs a function that will determine the total energy used from the beginning of the month to time .

  1. If time , no electricity has been used. Write an equation for that can be used to calculate the amount of electricity that has accumulated as a function of time. What is the relationship between the equations for and ?

    Notice that lower-case, , is a rate function.

  2. Use your equation for to calculate the total amount of electricity used during this month.

    Assume the month has days.

    'Total electrical consumption' is another way to say 'accumulated power.'

  3. Use your calculator to examine the graph of for this -day period. Then calculate the average amount of electricity used per day during this month. Does you answer match that in problem 6-144? How is this rate represented geometrically on the graph?

    Make sure that this graph agrees with your function for .

    First quadrant, Increasing curve, starting at the origin, concave up, ending at the approximate point (30, comma 325).