Based upon market research, the hawthone company has determined that consumers are willing to purchase 121 units of their portable media player each week when the price is set at s96.90 per unit. at a unit price f 40.20,cosumers are wiling to buy 310 units per week (a) determine the weekdy denund equation for this product, ansuming price, p, and quantity, x, are inearly related b) determine the weekdy revenue fanction a(x) of wnits consumers will demand weekly when the price is $50.70 per portable media player d determine the mumber of ts consumers will demand weekly when the revenue is maximieed )detormine the price of each unit when the revene is maximized

What is the slope of the line shown below?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Which of these figures must be a rectangle?