Please Help....

A hard-boiled egg at 98℃ is placed in a sink of 18℃ water to cool. After 5 minutes, the eggs temperature is found to be 38° C.
a) Find the value of P in Newton’s Law of Cooling.
b) Find the value of the constant k rounded to nearest hundredth.

c) What is the temperature after 3 minutes?
d) How long does it take the egg to cool to 25℃ ?

P, k? wouldn't that depend on how it is written, and in what language?

T(t)=18+80e^-kt

I have no idea what you mean as P.

for k, 38=18+80e^-k5
ln 38-ln18=ln80-5k
solve for k

To find the answers to the questions, we can use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between the object's temperature and the surrounding temperature.

a) P in Newton's Law of Cooling represents the temperature difference between the object's temperature and the surrounding temperature at a given time. In this case, P = (T - Ts), where 'T' is the temperature of the object and 'Ts' is the surrounding temperature. From the given information, after 5 minutes, the egg's temperature is 38℃ and the surrounding temperature is 18℃. Thus, P = (38℃ - 18℃) = 20℃.

b) The constant 'k' in Newton's Law of Cooling represents the cooling rate or the speed at which the object cools. Mathematically, k = [(ln(T - Ts) - ln(T0 - Ts))/t], where 'T' is the final temperature, 'T0' is the initial temperature, 'Ts' is the surrounding temperature, and 't' is the time taken to cool. In this case, the initial temperature is 98℃, the final temperature is 38℃, and the time taken to cool is 5 minutes. Therefore, k = [(ln(38℃ - 18℃) - ln(98℃ - 18℃))/5]

c) To find the temperature after 3 minutes, we can use the same formula mentioned above. We know the initial temperature (98℃), the final temperature (38℃), and the time taken in minutes (3). Plugging these values into the formula will give us the answer.

d) To find out how long it takes for the egg to cool to 25℃, we need to find the time taken (t) using the same formula as in part b. We know the initial temperature (98℃), the final temperature (25℃), and the constant 'k'. Plugging these values into the formula will give us the time taken to cool to 25℃.