P=2+98e0.075t15000 where t is measured in months. (a) How many fish were initially stocked in the lake? [21] (b) How many months does it take for the fish population to reach 5000 ? (c) Find the rate at which the number of fish in the lake is changing after one month. Include units. Interpret the meaning of your result. [1] (d) What is the limiting fish population in the lake as time increases without bound? [21] (e) During which month is the fish population increasing at the fastest rate? (Use the shortcut rule!) [21]