Factory began dumping toxic waste materials into a countryside lake. Before the dumping began, the estimated population of striped bass in the lake was 40,000. Since the dumping of toxic waste materials began, the population has decreased by one-half every month. Determine the equation that represents this situation and use it to decide which of the following graphs represents the population of striped bass, f(x), x months after the factory began dumping toxic waste materials into the lake.

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.