### Home > CALC > Chapter 6 > Lesson 6.4.3 > Problem 6-160

The function

*k*(*t*) = 8 − cos*t*+ 0.01*t*^{2}+ 0.01*t*helped Kira determine the*rate*at which electricity was being used on any day*t*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*K*(*t*) that will determine the total energy used from the beginning of the month to time*t*. Homework Help ✎Find a function

*K*(*t*) that will accumulate the power used over time*t*. Be sure that*K*(0) = 0. What is its relationship to*k*(*t*)?Use

*K*(*t*) to find the total electrical energy used during this month.Sketch a graph of

*K*(*t*) for this 30-day period.Calculate the average power used in kilowatts for this month. Did your answer match that in problem 6-151? How is this rate represented geometrically in the graph?

Notice that lower-case, *k*(*t*), is a rate function.

Assume the month has 30 days.

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

Make sure that this graph agrees with your function for *K*(*t*).