MATH137 Lecture : Exponential Growth, Max & Min Values, Fermat's Theorem, Closed Inteval Method

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Jennifer Nissen

Document Summary

We know that if , is a constant then. The only solution to the differential equation is. Suppose we have a bacteria culture initially containing 100 cells and growing at a rate proportional to its size. Let represent the of cells in the culture at time ( hours) What is the growth rate at 3 hrs? cells/hour c) Radiation substances decay at a rate proportional to their mass. An object cools at a rate proportional to the difference in temperature between the object and its surroundings. Let be the temperature difference at time . Problems where we"re interested in the rate of change of a quantity (ie. its derivative) given the rate of change (derivative) of a related quantity. A cube has volume , side length . The side length expands as time passes (and so increases). Find an expression relating the rate at which the volume changes and the rate the side length changes.