A classmate is building a mathematical model for the temperature in his home during the summer. He explains that, without air conditioning, his home is hottest at 3:00 p.m. His model considers temperature, T, in degrees Fahrenheit, as a function of the number of hours since 6:00 a.m., h. He produces the equation, T (h) = -12 cos( (h – 1)) + 75. Why might his equation be invalid for this situation? O The period of 12 hours indicates that two highs occur throughout the day. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The amplitude must be incorrect. O The sine function is more accurate in modeling these temperatures. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The horizontal shift must be incorrect.

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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.