The quantity Q(t) of a drug in the bloodstream, in mg, at hour t, decays exponentially, as given in the graph and the table below. Assume the pattern in the table holds. Complete parts (a) through (d) below. (a) Fill in the table. Hint: Some of the values are listed on the vertical axis. (Type an integer or decimal rounded to one decimal place as needed.) Amount Q, Time, t, (hours) 102.47 (mg) Number 3 102.4 6. 51.2 9. 25.6 12 12.8 51.2- 15 2.274 18 .8503 25.6- 6 9. 12 15 18 21 24 (b) Report the half-life. Use the pull-down menu to report the units. The half-life is 37 hours (c) Write a formula which gives Q as a function of t. The parameters in the formula should not contain rounded values. Include 0.5 in your formula. Q = ABP (Your answer involves 0.5, real numbers, and a lower case t.) TIP: If desired, click on the Plot icon ( F) next to the answer box to graph your response. (Although your answer may match the graph, it will be counted incorrect if it is not in the form requested.) (d) Estimate the length of time until the amount of the drug in the patient's bloodstream is 0.4 mg. After Number hours, the amount of drug in the bloodstream is 0.4 mg. (Type an integer or decimal rounded to one decimal place as needed.)
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
b-d
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