Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence. d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 x = − b ± b 2 − 4 a c 2 a x = − b 2 a arbitrary binomial coefficient conjecture counterexample deductive reasoning equivalent expanded form exponential decay exponential function exponential growth f(x) factored form factoring factors function growth factor hypotenuse inductive reasoning inverse variation isosceles margin of error parabola parameters perfect squares polynomial prime polynomial profit quadratic function revenue right triangle standard form symmetry terms trinomial vertex zero In an_______________ equation like y = a · b x , a will be positive and the value of b will be greater than 1.
Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence. d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 x = − b ± b 2 − 4 a c 2 a x = − b 2 a arbitrary binomial coefficient conjecture counterexample deductive reasoning equivalent expanded form exponential decay exponential function exponential growth f(x) factored form factoring factors function growth factor hypotenuse inductive reasoning inverse variation isosceles margin of error parabola parameters perfect squares polynomial prime polynomial profit quadratic function revenue right triangle standard form symmetry terms trinomial vertex zero In an_______________ equation like y = a · b x , a will be positive and the value of b will be greater than 1.
Solution Summary: The author explains that in an exponential growth equation like y=acdot bx, a will be positive and the value of b is greater than 1.
Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence.
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
x
=
−
b
±
b
2
−
4
a
c
2
a
x
=
−
b
2
a
arbitrary
binomial
coefficient
conjecture
counterexample
deductive reasoning
equivalent
expanded form
exponential decay
exponential function
exponential growth
f(x)
factored form
factoring
factors
function
growth factor
hypotenuse
inductive reasoning
inverse variation
isosceles
margin of error
parabola
parameters
perfect squares
polynomial
prime polynomial
profit
quadratic function
revenue
right triangle
standard form
symmetry
terms
trinomial
vertex
zero
In an_______________ equation like
y
=
a
·
b
x
,
a
will be positive and the value of b will be greater than 1.
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
4. Solve the system of equations and express your solution using vectors.
2x1 +5x2+x3 + 3x4 = 9
-x2+x3 + x4 = 1
-x1-6x2+3x3 + 2x4
= -1
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