The population of fish in a lake declines at rate 8% every year. Let be the population of fish as a function of time in years. Suppose that the population of fish in the lake is 20 millions in the beginning. How many years the population of fish in the lake has less than half of the initial population?
of a fish population is the total mass of the member of the population at time 
. It is the product of the number of individuals 
in the population and the average mass 
of a fish at time t.In the case of guppies, breeding occurs continually. Suppose that at time 
weeks the population is 820 guppies and is growing at a rate of 50 guppies per week, while the average mass is 1.2 g and is increasing at a rate of 0.14 g/week. At what rate is the biomass increasing when 
for any given time, 
. They also measured that the amount of fish in that given area is changing at a rate of 
. If the change in the shark's consumption rate is the same as the change in the fish's spawning rate, there will not be enough for fish for the sharks. Will there ever be enough for fish for the sharks?