Looking up a skyscraper, you notice the lights going out in its windows at night. Let W(t) = the number of windows that are lit, where t = # hours after 6pm, and suppose W (t) satisfies the differential equation dW = kW t, where k is a constant. dt (a)  At 6 p.m. there are 360 lit windows, and an hour later, there are 320 lit windows. Solve the differential equation to find a formula for W (t). *******USE dW/kW=tdt (b)  How many windows are still lit at 10pm on the same night? (Round your answer to a whole number.) (c)  Determine at what time will there be only 1 lit window.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.