Suppose that the amount (in gallons) of water in a tank is given by f(t) = 60e^−.1t, where t is in hours. How much water is in the tank at t= 0? After 1 hour? What is the average amount of water in the tank in the first 24 hours?

The half-life of a radioactive substance is 37 hours. If f ( t ) = a e ^ k t gives the amount of substance in a lab sample after t hours, what is the correct value of k? Give your answer as a decimal with at least three places of accuracy to the right of the decimal point.

An oil tanker is leaking oil at a rate ofL ′ ( x ) = x e ^(− x/2)barrels per hour, where x is the time in hours after the tanker has hit a hidden rock (at x = 0). How many barrels will the ship leak on the first day?

A service station currently has 120 cases of motor oil. Over the next six months inventory of oil will be recorded monthly. Assume that the inventory is given by f(t)=120e^(−0.6t), where tt is the number of months from the present. Answer the following questions, rounding your answer to the nearest tenth. b) How many cases of oil are left at the end of the six-month period? Answer: c) What is the average number of cases in inventory over the six-month period? Answer: