![]() ![]() You can be paid 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day, and so on, doubling the amount you are paid each day. You can be paid $500 per day or Option 2. Suppose you are hired for a one month job (30 days, working every day) and are given two options to be paid. There is an old question that is often used to introduce the power of geometric growth. Let \(Q(n)\) be the amount (in mg) of warfarin in the body before the \((n+1)\)st dose of the drug is administered.Įxplain why \(Q(2) = (5+Q(1)) \times 0.08\) mg. Assume that at the end of a 24 hour period, 8% of the drug remains in the body. The drug is absorbed by the body and some is excreted from the system between doses. Suppose warfarin is taken by a particular patient in a 5 mg dose each day. The level of warfarin has to reach a certain concentration in the blood in order to be effective. Warfarin is an anticoagulant that prevents blood clotting often it is prescribed to stroke victims in order to help ensure blood flow. In Example7.12, we see an example of a sequence that is connected to a sum. Many important sequences are generated by addition. Under what conditions does a geometric series converge? What is the sum of a convergent geometric series? What is a partial sum of a geometric series? What is a simplified form of the \(n\)th partial sum of a geometric series? Section 7.2 Geometric Series Motivating Questions Population Growth and the Logistic Equation.Qualitative Behavior of Solutions to DEs.An Introduction to Differential Equations.Physics Applications: Work, Force, and Pressure.Area and Arc Length in Polar Coordinates.Using Definite Integrals to Find Volume by Rotation and Arc Length.Using Definite Integrals to Find Area and Volume. ![]()
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