A tub of ice cream initially has a temperature of 25 F. It is left to thaw in a room that has a temperature of 73 F. After 10 minutes, the temperature of the ice cream has risen to 32 F. After how many minutes (to the nearest minute) with the temperature of the ice cream be 47 F? The ice cream will be 47 F after minutesA bacteria culture starts with 860 bacteria and grows at a rate proportional to its size. After 5 hours there will be 4300 bacteria. (a) Express the population P after t hours as a function of t. P(t)= 860e0.3219t (b) What will be the population after 9 hours? bacteria (c) How long will it take for the population to reach 1650? Give your answer accurate to at least 2 decimal places. hoursA roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit. Give answers accurate to at least 2 decimal places. (a) If the temperature of the turkey is 154 Fahrenheit after half an hour, what is its temperature after 45 minutes? Fahrenheit (b) When will the turkey cool to 100 Fahrenheit? hours.An unknown radioactive element decays into non-radioactive substances. In 960 days the radioactivity of a sample decreases by 46 percent. (a) What is the half-life of the element? half-life: (days) (b) How long will it take for a sample of 100 mg to decay to 62 mg? time needed: (days)\fNewton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a cup of coffee begins at 185 degrees and, after sitting in room temperature of 61 degrees for 12 minutes, the coffee reaches 180 degrees. How long will it take before the coffee reaches 165 degrees? Include at least 2 decimal places in your