For the graph seen at (1:27), what is the y-intercept? What is happening at this point in the race between the tortoise and the hare? After 4 hours the tortoise has traveled 2 miles. How can you use the rate of change, or slope, to explain where he would be at 6 hours?
Using the equation y = 1/2x, how many miles (y) has the tortoise traveled after 10 hours (x)?
What is the equation of the line for the hare in slope-intercept form?
How many solutions does this graph have? Why?
How did this video help you understand solutions to systems of equations?

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?