The inequality x ≥ 25 can be used to represent the distance an athlete runs each week, where x is the distance in miles. Which of these statements best describe the distance run by the athlete each week?

1. The distance is more than 25 miles.
2.The distance is no more than 25 miles.
3.The distance is at least 25 miles.
4.The distance is less than 25 miles.

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?