Suppose that an object with an initial temperature π0 is placed in an atmosphere of temperature ππ. Newtonβs Law of Cooling states that the temperature of the object after π‘ minutes is given by the function π(π‘) = ππ + (π0 β ππ )π βππ‘, where π is a positive constant that depends on the type of object. a. A restaurant serves a cup of coffee at a temperature of 180Β°πΉ. If the manager of the restaurant keeps the thermostat set at 67Β°πΉ, what will be the temperature of the coffee after 30 minutes if no one drinks it? (Assume that π = 0.065.) Round to the nearest whole number and include units in your answer. b. At the same restaurant, a bowl of chili is served at 185Β°πΉ. If a customer cannot eat it at a temperature higher than 106Β°πΉ, how long will he need to wait? (Assume that π = 0.13.) Round to the nearest whole number and include units in your answer.
Second one
106 = 67 + ( 185 - 67)e(-..13 * t) subtract 67 from both sides
39 = ( 118)e(-.065 * t) divide both sides by 118
(39/118) = e (-.13 * t) take the Ln of both sides
Ln ( 39/118) =Ln e (-.13 * t) and we can write
Ln ( 39/118) = (-.13 * t) Ln e (Ln e =1....we can ignore this )
Ln ( 39/118) = -.13 * t divide both sides by -.13
Ln (39/118) /-.13 = t β 9 min