An object dropped from rest from the top of a tall building on Planet X falls a distance d (t )equals 8 t squared feet in the first t seconds. Find the average rate of change of distance with respect to time as t changes from t 1equals2 to t 2equals5. This rate is known as the average velocity, or speed. The average velocity as t changes from 2 to 5 seconds is nothing StartFraction feet Over sec EndFraction .

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?