Consider a 35°F object placed in a 64°F room. a. Write a differential equation for T, the temperature of the object at time t, using k > 0 for the constant of proportionality, and wri your equation in terms of T, k, and t. T' = k(T-1) b. Give the general solution to the differential equation found in Part a. Simplify your solution in terms of an unspecified constant C appears as the coefficient of an exponential term and the constant of proportionality k. T = c. The temperature of the object is 35°F initially and 42°F one hour later. Find the temperature of the object after 3 hours. T(3) = degrees F

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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.