1. At time t = 0, a popsicle is put into a 40-degree refrigerator. After ten minutes, its temperature is 4 degrees. After 30 minutes, its temperature is 15 degrees. Find T(t), the temperature of the popsicle at time t. Assume Newton's law of cooling. See an example.2. A radioactive substance has a half-life of 750 years. How long does it take for a sample of that substance to decay to only 20% of its original amount? Hint: because we're only talking percentages, we don't even need to know the starting amount; you can, if you want, take it to be any amount you want. See an example.3. The half-life of a radioactive substance is 300 years. Find the quantity Q(t) of the substance remaining at time t > 0 if Q(0) = 30 g. See an example.4. A 400 deg F pizza is placed on the counter of a 72 deg F kitchen. At exactly 6:15 pm, the temp of the pizza is 320 deg F. At exactly 6:30 pm, the temp of the pizza is 190 deg F. At what time was the pizza placed on the counter? Assume Newton's law of cooling. Round to the nearest minute5. Suppose a tank contains 200 gallons of brine containing 2 lb of salt. At time t = 0, pure water is pumped into the tank at a rate of 4 gallons per minute. The resulting mixture is then drained at a rate of 4 gallons per minute. Find A(t), the amount of salt in the tank at time t. See an example.6. At time t = 0, a large tank has 40 gallons of brine in it containing 4 lb of salt. Brine at a concentration of 0.2 lb per gallon is pumped into the tank at a rate of 1 gallon per minute. The resulting mixture is pumped out of the tank at a rate of 2 gallons per minute. What is the concentration of salt in the tank when the tank runs dry? In other words, find lim A(t) where A(t) is the amount of salt in the tank at toty W (t) time t, W(t) is the amount of fluid in the tank at time t, and t, is the time at which the tank runs dry