Suppose a cup of coffee is poured from a freshly-brewed pot and left to cool in a 75-degree room. Let the temperature (in °F) of the coffee be given by the function T(t) = 105(0.9634)^t + 75 where t is the time in minutes (t ≥ 0) the cup of coffee has been cooling after being poured. Use the equation T(t) = 100 to complete the following. a.) Use Newton’s method with an initial guess of t1 = 20 to estimate the solution to the equation, correct to six decimal places. (hint: Newton’s method only works for equations of the form f(x) = 0) b.) Interpret the solution from part (a) in context.

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.