The Los Angeles Zoo plans to transport a California sea lion to the San Diego Zoo. The animal will be wrapped in a wet blanket during the trip. At any time t, the blanket will lose water (due to evaporation) at a rate proportional to the amount f (t) of water in the blanket, with constant of proportionality k = -.3. Initially, the blanket will contain 2 gallons of seawater.

(a) Set up the differential equation satisfied by f (t).

(b) Use Euler’s method with n = 2 to estimate the amount of moisture in the blanket after 1 hour.

(c) Solve the differential equation in part (a) and compute f (1).

(d) Compare the answers in parts (b) and (c) and approximate the error in using Euler’s method.