The amount of charge passing through a surface, given by a function Q(t), is measured in coulombs C. The current is the rate at which charge flows through a surface. This function is I(t) and is measured in amperes, A, or coulombs per second, C/s. If a current for a certain surface is modeled by the function I(t) = 6t² + 6t + 5 for t ≥ 0, how much charge passes through the surface after 10 seconds? Provide your answer below: Coulombs

A dead body was found within a closed room of a house where the temperature wasa constant 70◦F . At the time of discovery the core temperature of the body wasdetermined to be 85◦F . One hour later a second measurement showed that the coretemperature of the body was 80◦F. Assume that the time of death corresponds to t = 0and the core temperature at the time was 98.6◦F. Determine how many hours elapsedbefore the body was found. (Use Newton’s Law of Cooling and let t1 > 0 denote thetime that the body was discovered

At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?

2. Caffeine is eliminated from the body at a continuous rate of approximately 17% per hour. A standard cup of coffee contains 150mg of caffeine.  a) Write a formula for the amount of caffeine C in mg as a function of the number t of hours after drinking a cup of coffee.  b) Find the number of hours (to the nearest hour) it makes for half of the caffeine from a cup of coffee to be eliminated from the body.  c) Find the number of hours (to the nearest hour) it takes for only 1.5mg of the caffeine from a cup of coffee to remain in the body.