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the table below shows the distance y, in miles, traveled by a toy car in x minutes:

time (x) (minutes) 10 20 30 40
distance (y) (miles) 4 8 12 15

part a: what is the most likely value of the correlation coefficient of the data in the table? based on the correlation coefficient, describe the relationship between time and distance traveled by the toy car. (4 points) [choose the value of correlation coefficient from 1, 0.99, 0.5, 0.02]
part b: what is the value of the slope of the graph of distance versus time between 10 minutes and 30 minutes, and what does the slope represent? (3 points)
part c: does the data in the table represent correlation or causation? explain your answer. (3 points)

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?