Heather is going to rent a truck for one day. There are two companies she can choose from and they have the following prices. Company A has no initial fee but charges 70 cents for every mile driven. Company B charges an initial fee of $75 and an additional 60 cents for every mile driven. For what mileages will Company A charge more than Company B. Use m for the number of miles driven and solve your inequality for m.​

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?