{Use of Tech} Power and energy Power and energy are often used...

Question

{Use of Tech} Power and energy Power and energy are often used interchangeably, but they are quite different. Energy is what makes matter move or heat up. It is measured in units of joules or Calories, where 1 Cal=4184 J. One hour of walking consumes roughly 10⁶J, or 240 Cal. On the other hand, power is the rate at which energy is used, which is measured in watts, where 1 W=1 J/s. Other useful units of power are kilowatts (1 kW=10³ W) and megawatts (1 MW=10⁶ W). If energy is used at a rate of 1 kW for one hour, the total amount of energy used is 1 kilowatt-hour (1 kWh=3.6×10⁶ J) Suppose the cumulative energy used in a large building over a 24-hr period is given by E(t)=100t+4t²−t³ / 9kWh where t=0 corresponds to midnight.
c. Graph the power function and interpret the graph. What are the units of power in this case?

c. Graph the power function and interpret the graph. What are the units of power in this case?

Accepted Answer

Welcome back, everyone. In this problem, a solar panel generates energy according to the function A of T equals 60T minus 2 T 2 plus T cubed divided by 6 kilowatt hours, where T is the timing hours after sunrise. The power generated by the solar panel is the derivative of the energy function. Graph the power function on the interval open bracket 0 24 closed bracket using a graphing utility and interpret it. And here we have a graph that we can use to plot our utility, to plot our power functions, right. Now, what are we trying to plot again? We want to graph the power function. We are already given the function that tells us how the solar panel generates energy, and we're told that the power generated by the solar panel is the derivative of the energy function. So we can differentiate EFT, plot it on our graph, and then interpret what we see. So first, let's differentiate EFT, our energy function, OK? So differentiating EFT. With respect to tea, OK. Then The derivative is going to be equal to 60. The derivative of 60T is 60. The derivative of -2 squad is -40, and the derivative of T cubed divided by 6 will be 3 T 2 divided by 6, which will give us T2 divided by 2. This is the power function, OK, for coming from our energy function. Now that we have the power function, we can use it to plot on our graph. Since we're using our graphing utility, I can go ahead and plot here what I got from our graphing utility, and it would look something like this, OK? Now when we look at our plot, what do we notice? Well, notice here that our minimum value is at T equals 4. That means from the graph we can tell that the power attained, let's write that thought, the power attained, it's the minimum value. Minimum value. Add T equals 4 hours. Now what do you notice after that? Well, after the minimum value, then notice that it starts to increase, OK? So then we can say that the power. Started increasing, OK, started increasing. After T equals 4 hours. This is what our pore function tells us about our solar panel. Or how the power is generated by the solar panel. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Energy vs. Power

Cumulative Energy Function

Graphing Power Function

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