1) Translate the following equation into English, using m to mean mass, t to mean time and k to be a constant:
dm(t)dt=-km(t)
2) The height of Jack's beanstalk is an exponential function of time. If the initial height is 3 ft, and if the doubling time is 4 hours, graph the height of the beanstalk as a function of time.
3) I have foolishly invested in smallpox vaccine. I initially invested 10,000 dollars. However, since the disease smallpox has been nearly eradicated, the value of the vaccine is decaying exponentially, with a half-life of 2.5 weeks. Graph the value of my vaccine as a function of time.
4) What does the science principle that models should be "simple" suggest about the nature of the equations that represent "simple" models? (This question is a challenge one in that it is not specifically addressed in the book. Please make your best attempt.)