Question

The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; t is measured in hours starting at midnight.)

(a) What was the power consumptions at 6 AM? At 6 PM?

(b) When was the power consumption the lowest? When was it the highest? Do these times seem reasonable?

Short answer

a. At 6 AM, the power consumption is 500 MW, and at 6 PM, the power consumption is 730 MW.

b. The lowest power consumption is at 4 AM, whereas the highest power consumption is at 12 PM.

Step-by-step solution

Find the solution for part (a)

From the graph, at 6 AM, i.e., \(t = 6\), the power consumptions is \(P = 500\;{\rm{MW}}\).

Similarly, at 6 PM, i.e., \(t = 18\), the power consumption is approximately \(730\;{\rm{MW}}\).

Sketch the graph of temperature

From the graph between P and t, the lowest value of P occurs at \(t = 4\), i.e., at 4 AM.

Similarly, the power consumption is highest at \(t = 12\), i.e., 12 PM.

These times are reasonable considering the power schedule of most individuals and businesses.