Three math questions:

1) Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 166 degrees in a room at 60 degrees, determine when the coffee reaches a temperature of 136 degrees.
The coffee will reach a temperature of 136 degrees in ___ minutes

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2) A thermometer is taken from a room where the temperature is 24oC to the outdoors, where the temperature is −13oC. After one minute the thermometer reads 5oC.
(a) What will the reading on the thermometer be after 4 more minutes?

__

(b) When will the thermometer read −12oC? minutes after it was taken to the outdoors.

__

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3) Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5600. The number of fish tripled in the first year.

(a) Assuming that the size of the fish population satisfies the logistic equation

dP/dt = KP (1- P/K) ,

dPdt=kP(1−PK)

determine the constant k, and then solve the equation to find an expression for the size of the population after t years.

k=

p(t) =

(b)
(b) How long will it take for the population to increase to 2800 (half of the carrying capacity)?

It will take____ years

thanks